Find the derivatives of the function defined as follows. y=sin⁡e10x

Question

Find the derivatives of the function defined as follows.  y=sin⁡e10x

Anot1954 · Accepted Answer

Step 1
Use the chain rule of derivation to find the derivative of

y = \sin (e^{10 x})

.
Find the derivative of

\sin (x)

assuming

e^{10 x}

as x and then substitute

e^{10 x}

for x.

y = \sin (e^{10 x})

\frac{d y}{d x} = \frac{d (\sin (e^{10 x})} {d x}}{}

= \cos (e^{10 x})

Step 2
Using the chain rule derivate the parameter inside cosine function by first finding derivative of

e^{x}

assuming 10x as x then find the derivative of 10x with respect to x and multiplying all the values of the derivatives to find the derivative of the function

y = {\sin e}^{10 x}

y = \sin (e^{10 x})

\frac{d y}{d x} = \frac{d (\sin (e^{10 x})} {d x}}{}

= \cos (e^{10 x})

= (\cos (e^{10 x})) (\frac{d (e^{10 x})}{d x}) (\frac{d (10 x)}{d x})

= \cos (e^{10 x}) (e^{10 x}) (10)

= 10 e^{10 x} \cos (e^{10 x})

Find the derivatives of the function defined as follows. y=\sin e^{10x}

Answered question

Answer & Explanation

New Questions in Differential Calculus