HSC Science (General) १२ वीं कक्षा - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Find the derivative of the function y = f(x) using the derivative of the inverse function x = f^-1(y) in the following: y = `root(3)(x - 2)`

Find the derivative of the function y = f(x) using the derivative of the inverse function x = f^–1(y) in the following:

y = log(2x – 1)

Find the derivative of the function y = f(x) using the derivative of the inverse function x = f^–1(y) in the following: y = 2x + 3

Find the derivative of the function y = f(x) using the derivative of the inverse function x = f^–1(y) in the following: y = e^x – 3

Find the derivative of the function y = f(x) using the derivative of the inverse function x = f^–1(y) in the following: y = e^2x-3 

Find the derivative of the function y = f(x) using the derivative of the inverse function x = f^–1(y) in the following: y = `log_2(x/2)`

Find the derivative of the inverse function of the following : y = x²·e^x 

Find the derivative of the inverse function of the following : y = x cos x

Find the derivative of the inverse function of the following : y = x ·7^x 

Find the derivative of the inverse function of the following : y = x² + log x

Find the derivative of the inverse function of the following : y = x log x

Find the derivative of the inverse of the following functions, and also find their value at the points indicated against them. y = x⁵ + 2x³ + 3x, at x = 1

Find the derivative of the inverse of the following functions, and also find their value at the points indicated against them. y = e^x + 3x + 2

Find the derivative of the inverse of the following functions, and also find their value at the points indicated against them. y = 3x² + 2logx³ 

Find the derivative of the inverse of the following functions, and also find their value at the points indicated against them. y = sin(x – 2) + x² 

If f(x) = x³ + x − 2, find (f⁻¹)'(0).

Using derivative, prove that: tan ^–1x + cot^–1x = `pi/(2)`

Using derivative, prove that: sec^–1x + cosec^–1x = `pi/(2)`    ...[for |x| ≥ 1]

Choose the correct option from the given alternatives :

If g is the inverse of function f and f'(x) = `(1)/(1 + x)`, then the value of g'(x) is equal to :

If y = f(x) is a differentiable function of x, then show that `(d^2x)/(dy^2) = -(dy/dx)^-3.("d^2y)/(dx^2)`.