Arts (English Medium) Class 11 - CBSE Question Bank Solutions for Mathematics

Find the rate at which the function f (x) = x⁴ − 2x³ + 3x² + x + 5 changes with respect to x.

\[\text{ If } y = \frac{2 x^9}{3} - \frac{5}{7} x^7 + 6 x^3 - x, \text{ find } \frac{dy}{dx} at x = 1 .\] 

If for f (x) = λ x² + μ x + 12, f' (4) = 15 and f' (2) = 11, then find λ and μ. 

For the function \[f(x) = \frac{x^{100}}{100} + \frac{x^{99}}{99} + . . . + \frac{x^2}{2} + x + 1 .\]

x³ sin x 

x³ e^x 

x² e^x log x 

xⁿ tan x 

xⁿ log_a x 

(x³ + x² + 1) sin x 

sin x cos x

\[\frac{2^x \cot x}{\sqrt{x}}\] 

x² sin x log x 

x⁵ e^x + x⁶ log x 

(x sin x + cos x) (x cos x − sin x) 

(x sin x + cos x ) (e^x + x² log x) 

(1 − 2 tan x) (5 + 4 sin x)

(1 +x²) cos x

sin² x 

log_x² x