PUC Science कक्षा ११ - Karnataka Board PUC Question Bank Solutions for Mathematics

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

\[\frac{x^3}{3} - 2\sqrt{x} + \frac{5}{x^2}\]

e^x log a + e^a long x + e^a log a

(2x² + 1) (3x + 2) 

 log₃ x + 3 log_e x + 2 tan x

\[\left( x + \frac{1}{x} \right)\left( \sqrt{x} + \frac{1}{\sqrt{x}} \right)\] 

\[\left( \sqrt{x} + \frac{1}{\sqrt{x}} \right)^3\] 

\[\frac{2 x^2 + 3x + 4}{x}\]