PUC Science Class 11 - Karnataka Board PUC Question Bank Solutions for Mathematics

Differentiate each of the following from first principle:

e^−x

Differentiate  of the following from first principle:

e^3x

Differentiate  of the following from first principle:

 e^ax + b

x e^x

Differentiate  of the following from first principle: 

− x

Differentiate of the following from first principle:

(−x)⁻¹

Differentiate  of the following from first principle:

sin (x + 1)

Differentiate  of the following from first principle:

\[\cos\left( x - \frac{\pi}{8} \right)\]

Differentiate  of the following from first principle:

 x sin x

Differentiate of the following from first principle:

 x cos x

Differentiate  of the following from first principle:

sin (2x − 3)

Differentiate each of the following from first principle:

\[\sqrt{\sin 2x}\] 

Differentiate each of the following from first principle:

\[\frac{\sin x}{x}\]

Differentiate each of the following from first principle: 

\[\frac{\cos x}{x}\]

Differentiate each of the following from first principle:

 x² sin x

Differentiate each of the following from first principle:

\[\sqrt{\sin (3x + 1)}\]

Differentiate each of the following from first principle: 

sin x + cos x

Differentiate each of the following from first principle:

x² e^x 

Differentiate each of the following from first principle: 

\[e^{x^2 + 1}\]

Differentiate each  of the following from first principle:

\[e^\sqrt{2x}\]