Differentiate the following with respect to x:

Given,

f(x) =

using change of base formula for log, we can write –

log_x 3 = (log_e 3)/(log_e x)

∴ f(x) =

⇒ f(x) =

we need to find f’(x), so differentiating both sides with respect to x –

∴ )

Using algebra of derivatives –

⇒ f’(x) =

Use the formula:

∴ f’(x) = 2( – cosec x cot x) + 8(2^x log_e2) – 4/(log_e3) (1/x)

⇒ f’(x) =

∴ f’(x) =