Question

Find the differentiation of √x cosX + cos(x³)​

Answer 1

Answer:

There are different methods to solve this.

I will use a simple method here.

Here you go :

Required Formulae :

1.) d/dx x^n = nx^(n - 1)

2.) d/dx cos x = -sin x

Let,

y = (cos x)^3

Let us ASSUME that cos x is ‘x' i. e. The variable with respect to which we will be differentiating.

Thus, using formula no. 1, we get,

dy/dx = 3(cosx)^2

But, cos x is not ‘x'.

Therefore, we will differentiate the part which we assumed to be ‘x’( in this case, cos x ) and multiply it in the above equation.

Thus,

dy/dx = 3(cosx)^2 * d/dx(cosx)

Thus,

dy/dx = 3(cosx)^2 * (-sinx) ….(using Formula no. 2)

Thus,

dy/dx = -3sinx(cosx)^2

Final Answer is:

dy/dx = -3sinx(cosx)^2

Answer 2

Answer:

Check the attachment for the answer...

hope this helps you...