Q2 of 168 Page 30

Differentiate the following with respect to x:
3^x + x³ + 3³

Given,

f(x) = 3^x + x³ + 3³

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) = 3^x log_e 3 – 3x^{3 – 1} + 0

⇒ f’(x) = 3^x log_e 3 – 3x²

Differentiate the following from first principles

Differentiate the following with respect to x:

x⁴ – 2sin x + 3 cos x

Differentiate the following with respect to x:

e^{x log a} + e^{a log x} + e^{a log a}

Differentiate the following with respect to x:3x + x3 + 33