Let, y = x⁵ e^x + x⁶ log x

Let, A = x⁵ e^x and B = x⁶ log x

∴ y = A + B

⇒

We have to find dA/dx first

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

u = x⁵ and v = e^x

∴ A = 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 = x⁵

∴ …equation 2 {∵ }

As, v = e^x

…equation 3 {∵ }

∴ from equation 1, we can find dy/dx

∴

⇒ {using equation 2 & 3}

Hence,

…..equation 4

Now, we will find dB/dx first

As we can observe that A is a product of two functions say m and n where,

m = x⁶ and n = log x

∴ B = mn

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 5

As, m = x⁶

∴ …equation 6 {∵ }

As, v = log x

…equation 7 {∵ }

∴ from equation 5, we can find dy/dx

∴

⇒ {using equation 6 & 7}

Hence,

…..equation 8

As,

∴ from equation 4 and 8, we have –