from a handpicked tutor in LIVE 1-to-1 classes

# Differentiate the function with respect to x. sin(x^{2 }+ 5)

**Solution:**

Let f(x) = sin (x^{2 }+ 5),

u(x) = x^{2}+ 5

f(x) = sin (x^{2 }+ 5),

u(x) = x^{2 }+ 5 and v(t) = sin t

Then, (vou)(x) = v(u(x)) = v(x^{2 }+ 5)

= tan (x^{2 }+ 5) = f(x)

Thus, f is a composite of two functions.

Put, t = u(x) = x^{2 }+ 5t

Then, we get

dv/dt = d/dt(sint)

= cos t = cos (x^{2 }+ 5) dt / dx

= d/dx (x^{2 }+ 5)

= d/dx (x^{2}) + d / dx (5)

= 2x + 0 = 2x

df / dx = dv / dt. dt / dx = cos (x^{2 }+ 5) × 2x = 2x cos (x^{2 }+ 5)

Alternate method:

d/dx [sin (x^{2 }+ 5)] = cos (x^{2 }+ 5).d / dx (x^{2 }+ 5)

= cos (x^{2 }+ 5).[d / dx (x^{2}) + d / dx (5)]

= cos (x^{2 }+ 5).[2x + 0]

= 2x cos (x^{2 }+ 5)

NCERT Solutions Class 12 Maths - Chapter 5 Exercise 5.2 Question 1

## Differentiate the function with respect to x. sin(x^{2 }+ 5)

**Summary:**

By chain rule of derivative, We have obtained the derivative of sin(x^{2 }+ 5) is 2x cos (x^{2 }+ 5)

visual curriculum