Question

Find the derivative of f(x)=sin4x from 1st principle

Answer 1

Step-by-step explanation:

Differential of sin4x can be calculated by chain rule.

Let us solve the above differential step by step:

Chain Rule General Steps:

Step 1

: Identify the inner and outer functions.

Here, the outer function is ‘sin’ and inner function is 4x.

Step 2:

Differentiate the outer function first. And write the inner function as it is.

12

The outer function is Sin.

Therefore,

Differtial of sin is cos. And on writing the inner function as it is,

we get,

Cos4x

Step 3:

Differentiate the inner function, and then multiply it to the outer function’s derivative.

Differentiating inner function 4x,

Derivative of 4x is 4.

Now, Multiplying inner function's derivation with outer function's derivative.

i.e., 4cos4x.

Hence,

The derivative of sin4x is 4cos4x.