Question

find the derivative of e^sinhx

Answer 1

dy / DX = e^sinhx. coshx .h is the answer
I will tell you method
first write the question I.e e^sinhx then write the derivative of sinhx then write the derivative of hx.i.e h and derivative of x is 1

Answer 2

Answer:

The correct answer will be -

$\frac{dy}{dx} = e^{sinh\ x}.cosh\ x$

Step-by-step explanation:

In the given problem we have to find the derivative of $y = e^{sinh\ x}$

here $sinh\ x$ is a hyperbolic function.

Also, It is given by -

$sinh\ x = \frac{e^x-e^{-x}}{2}$

Now, doing differentiation -

Take $u = sinh\ x$

from here -

$\frac{du}{dx} = cosh\ x$

so differentiating the problem which is given in the question using the product rule we will get -

$\frac{dy}{dx} = \frac{d}{dx} (e^u)\\\\= e^u\frac{du}{dx}$

putting the values -

$\frac{dy}{dx} = e^{sinh\ x}.cosh\ x$

This will be our answer.

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