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

Differentiate in two ways, using product rule and otherwise, the function (1 + 2 tan x) (5 + 4 cos x). Verify that the answers are the same. 

Differentiate each of the following functions by the product rule and the other method and verify that answer from both the methods is the same. 

 (3x² + 2)²

Differentiate each of the following functions by the product rule and the other method and verify that answer from both the methods is the same.

(x + 2) (x + 3)

Differentiate each of the following functions by the product rule and the other method and verify that answer from both the methods is the same.

(3 sec x − 4 cosec x) (−2 sin x + 5 cos x)

(ax + b) (a + d)²

(ax + b)ⁿ (cx + d)ⁿ 

\[\frac{x^2 + 1}{x + 1}\] 

\[\frac{2x - 1}{x^2 + 1}\] 

\[\frac{x + e^x}{1 + \log x}\] 

\[\frac{e^x - \tan x}{\cot x - x^n}\] 

\[\frac{a x^2 + bx + c}{p x^2 + qx + r}\] 

\[\frac{x}{1 + \tan x}\] 

\[\frac{1}{a x^2 + bx + c}\] 

\[\frac{e^x}{1 + x^2}\] 

\[\frac{e^x + \sin x}{1 + \log x}\] 

\[\frac{x \tan x}{\sec x + \tan x}\]

\[\frac{x \sin x}{1 + \cos x}\]

\[\frac{2^x \cot x}{\sqrt{x}}\] 

\[\frac{\sin x - x \cos x}{x \sin x + \cos x}\]

\[\frac{x^2 - x + 1}{x^2 + x + 1}\]