PUC Science इयत्ता ११ - Karnataka Board PUC Question Bank Solutions

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:

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

Differentiate each of the following from first principle:

\[e^\sqrt{ax + b}\]

Differentiate each of the following from first principle:

\[a^\sqrt{x}\]

Differentiate each of the following from first principle:

\[3^{x^2}\]

tan² x 

tan (2x + 1) 

 tan 2x 

\[\sqrt{\tan x}\]

\[\sin \sqrt{2x}\]

\[\cos \sqrt{x}\]

\[\tan \sqrt{x}\]

\[\tan \sqrt{x}\] 

x⁴ − 2 sin x + 3 cos x

3^x + x³ + 3³