Q. 35.0( 3 Votes )

# Differentiate the following functions with respect to x:

x^{2} e^{x} log x

Answer :

Let, y = x^{2} e^{x} log x

We have to find dy/dx

As we can observe that y is a product of three functions say u, v & w where,

u = x^{2}

v = e^{x}

w = log x

∴ y = uvw

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

By product rule, we have –

…equation 1

As, u = x^{2}

∴ …equation 2 {∵ }

As, v = e^{x}

…equation 3 {∵ }

As, w = log x

∴ …equation 4 {∵ }

∴ from equation 1, we can find dy/dx

∴

⇒ {using equation 2, 3 & 4}

Hence,

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