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Find the derivatives of each of the functions in Exercises 51–62. In some cases it may be convenient to do some preliminary algebra. (These exercises involve hyperbolic functions and their inverses.)

f(x)=sinesinh-1x

Short Answer

Expert verified

The derivative iscosesinh-1xesinh-1xx2+1.

Step by step solution

01

Step 1. Given information.

The given function isf(x)=sinesinh-1x.

02

Step 2. Preliminary Algebra.

We know,

ddx(sinx)=cosxddxsinh-1x=1x2+1ddxex=ex(fu)'(x)=f'(u(x))u'(x)

03

Step 3. Derivative.

The derivative of the function is,

ddxsinesinh-1x=cosesinh-1xddxesinh-1x=cosesinh-1xesinh-1xddxsinh-1x=cosesinh-1xesinh-1x1x2+1=cosesinh-1xesinh-1xx2+1

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