Q. 135.0( 1 Vote )

# Differentiate the following functions with respect to x:

Let, y =

We have to find dy/dx

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

u = sin x – x cos x and v = x sin x + cos x

y = u/v

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

By quotient rule, we have –

…equation 1

u = – (x cos x – sin x)

Using algebra of derivatives –

{using product rule}

…equation 2

As, v = x sin x + cos x

Using algebra of derivatives –

{using product rule}

…equation 3

from equation 1, we can find dy/dx

using equation 2 and 3, we get –

Hence,

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