Asked by: Ulyana Cristensen
science space and astronomy

What is the derivative of Sinh 2x?

Last Updated: 12th June, 2020

36
The derivative of sinh(u) sinh ( u ) with respect to u u is cosh(u) cosh ( u ) . Replace all occurrences of u u with 2x 2 x .

Click to see full answer.

Thereof, what is derivative of Sinh?

So, the derivatives of the hyperbolic sine and hyperbolic cosine functions are given by. (sinhx)′=(ex−e−x2)′=ex+e−x2=coshx,(coshx)′=(ex+e−x2)′=ex−e−x2=sinhx.

Secondly, what is the derivative of hyperbolic sine? Hyperbolic Functions

Function Derivative Graph
cosh(x) sinh(x)
tanh(x) 1-tanh(x)²
coth(x) 1-coth(x)²
sech(x) -sech(x)*tanh(x)

Secondly, how do you differentiate Cosh and Sinh?

Let g(x) = cosh x and h(x) = sinh x 2, function f is the quotient of functions g and h: f(x) = g(x) / h(x). Hence we use the quotient rule, f '(x) = [ h(x) g '(x) - g(x) h '(x) ] / h(x) 2, to find the derivative of function f.

What is the formula of Sinhx?

x = e x − e − x 2 sinh x = dfrac{e^x - e^{-x}}{2} sinhx=2ex−e−x? cosh ? x = e x + e − x 2 cosh x =dfrac{e^x + e^{-x}}{2} coshx=2ex+e−x?

Related Question Answers

Hasmik Curcan

Professional

What is COTX derivative?

The derivative of sec ? x displaystyle sec{{x}} secx is sec ? x tan ? x displaystyle sec{{x}} an{{x}} secxtanx and. The derivative of cot ? x displaystyle cot{{x}} cotx is − csc ? 2 x displaystyle-{{csc}^{2}{x}} −csc2x.

Yolando Sonko

Professional

What is Secx?

The cotangent of x is defined to be the cosine of x divided by the sine of x: cot x = cos x sin x . The secant of x is 1 divided by the cosine of x: sec x = 1 cos x , and the cosecant of x is defined to be 1 divided by the sine of x: csc x = 1 sin x .

Suresh Potsepkin

Explainer

How do you integrate by parts?

So we followed these steps:
  1. Choose u and v.
  2. Differentiate u: u'
  3. Integrate v: ∫v dx.
  4. Put u, u' and ∫v dx into: u∫v dx −∫u' (∫v dx) dx.
  5. Simplify and solve.

Aldara Payas

Explainer

What is the derivative of Secxtanx?

The derivative of sec(x) with respect to x is sec(x)tan(x) sec ( x ) tan ( x ) . The derivative of tan(x) with respect to x is sec2(x) sec 2 ( x ) .

Sidonio Arriero

Explainer

Does cosh ever equal zero?

Alternatively, you can simply observe that coshx is always non-zero, and the only solution comes from sinhx=0.

Aleidis Krupala

Pundit

What is Sinh 1x?

The hyperbolic sine function, sinhx, is one-to-one, and therefore has a well-defined inverse, sinh1x, shown in blue in the figure. By convention, cosh−1x is taken to mean the positive number y such that x=coshy.

Veselin Kusztal

Pundit

How do you differentiate Sinhx?

= 1/2 ex - 1/2 e-x = ( ex - e-x )/2 = sinh(x) Q.E.D. cosh(x) = sinh(x); tanh(x) = sinh(x)/cosh(x); Quotient Rule. = ( cosh(x) cosh(x) - sinh(x) sinh(x) ) / cosh2(x) = 1 - tanh2(x) Q.E.D. tanh(x) = 1 - tanh2(x); csch(x) = 1/sinh(x); sech(x) = 1/cosh(x); coth(x) = 1/tanh(x); Quotient Rule.

Steffanie Kornfeld

Pundit

What is an Arcsin?

Arcsin definition
The arcsine of x is defined as the inverse sine function of x when -1≤x≤1. When the sine of y is equal to x: sin y = x. Then the arcsine of x is equal to the inverse sine function of x, which is equal to y: arcsin x = sin-1 x = y.

Victoria Scholdt

Pundit

What is product rule in calculus?

The product rule is used in calculus when you are asked to take the derivative of a function that is the multiplication of a couple or several smaller functions. In other words, a function f(x) is a product of functions if it can be written as g(x)h(x), and so on. This function is a product of two smaller functions.

Ieda Almau

Pundit

What is meant by hyperbolic function?

a function of an angle expressed as a relationship between the distances from a point on a hyperbola to the origin and to the coordinate axes, as hyperbolic sine or hyperbolic cosine: often expressed as combinations of exponential functions.

Karoly Wehrstedt

Teacher

What is chain rule in calculus?

The chain rule states that the derivative of f(g(x)) is f'(g(x))⋅g'(x). In other words, it helps us differentiate *composite functions*. For example, sin(x²) is a composite function because it can be constructed as f(g(x)) for f(x)=sin(x) and g(x)=x².

Nagore Cia

Teacher

How do you derive the inverse of a hyperbolic function?

The standard way to derive the formula for sinh−1x goes like this: Put y=sinh−1x so that x=sinhy=ey−e−y2. Rearrange this to get 2x=ey−e−y, and hence e2y−2xey−1=0, which is a quadratic equation in ey. You then solve the quadratic and take logs (and take care with the ± sign you get with the roots of the quadratic).

Dalmacio Avdeichikov

Teacher

What is Sinh function?

Sinh is the hyperbolic sine function, which is the hyperbolic analogue of the Sin circular function used throughout trigonometry. It is defined for real numbers by letting be twice the area between the axis and a ray through the origin intersecting the unit hyperbola .

Odilo Mije

Reviewer

What is the derivative of E X?

Since the derivative of ex is ex, then the slope of the tangent line at x = 2 is also e2 ≈ 7.39.

Nonato Cosmen

Reviewer

How do you do implicit differentiation?

Summary
  1. To Implicitly derive a function (useful when a function can't easily be solved for y) Differentiate with respect to x. Collect all the dy/dx on one side. Solve for dy/dx.
  2. To derive an inverse function, restate it without the inverse then use Implicit differentiation.

Edeltraut Borau

Reviewer

What is the derivative of hyperbolic cosine?

The derivative of sinh x is cosh x and the derivative of cosh x is sinh x; this is similar to trigonometric functions, albeit the sign is different (i.e., the derivative of cos x is −sin x).