Differentiate the function with respect to x. cos(sin x)

Solution:

Let f(x) = cos (sin x),

u(x) = sin x and v(t) = cos⁡ t

Then, (vou)(x) = v(u (x))

= v(sin x)

= cos(sin x) = f(x)

Here, f is a composite function of two functions.

Put t = u(x) = sin x

⇒ dv/dt = d/dt[cos t]

= −sin t

= −sin(sin x)

dt/dx = d/dx (sin x) = cos x

By chain rule,

df/dx = dv/dt.dt/dx = −sin (sin x).cos x = −cos x sin (sin x)

Alternate method:

d/dx [cos (sin x)] = − sin (sin x).d/dx (sin x)

= − sin(sin x) × cos x

= − cos x sin (sin x)

NCERT Solutions Class 12 Maths - Chapter 5 Exercise 5.2 Question 2

Differentiate the function with respect to x. cos(sinx)

Summary:

The derivative of cos(sin x) with respect to x is − cos x sin (sin x). Here, f is a composite function of two functions