Q. 65.0( 1 Vote )

# Differentiate the following functions with respect to x:

(x^{3} + x^{2} + 1) sin x

Answer :

Let, y = (x^{3} + x^{2} + 1) sin x

We have to find dy/dx

As we can observe that y is a product of two functions say u and v where,

u = x^{3} + x^{2} + 1 and v = sin x

∴ y = uv

As we know that to find the derivative of product of two function we apply product rule of differentiation.

By product rule, we have –

…equation 1

As, u = x^{3} + x^{2} + 1

∴

⇒ …equation 2 {∵ }

As, v = sin x

…equation 3 {∵ }

∴ from equation 1, we can find dy/dx

∴

⇒ {using equation 2 & 3}

Hence,

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