Arts (English Medium) Class 12 - CBSE Question Bank Solutions for Mathematics

Find the values of x, y, z if the matrix A = `[(0, 2y, z),(x, y, -z),(x, -y, z)]` satisfy the equation A'A = I.

If the matrix A is both symmetric and skew symmetric, then ______.

Differentiate the function with respect to x. 

cos x . cos 2x . cos 3x

Differentiate the function with respect to x.

`sqrt(((x-1)(x-2))/((x-3)(x-4)(x-5)))`

Differentiate the function with respect to x.

(log x)^{cos x}

Differentiate the function with respect to x.

x^x − 2^{sin x}

Differentiate the function with respect to x.

(x + 3)² . (x + 4)³ . (x + 5)⁴

Differentiate the function with respect to x.

`(x + 1/x)^x + x^((1+1/x))`

Differentiate the function with respect to x.

(log x)^x + x^{log x}

Differentiate the function with respect to x.

`(sin x)^x + sin^(-1) sqrtx`

Differentiate the function with respect to x.

x^{sin x} + (sin x)^{cos x}

Differentiate the function with respect to x.

`x^(xcosx) + (x^2 + 1)/(x^2 -1)`

Differentiate the function with respect to x.

`(x cos x)^x + (x sin x)^(1/x)`

Find `bb(dy/dx)` for the given function:

x^y + y^x = 1

Find `bb(dy/dx)` for the given function:

y^x = x^y

Find `bb(dy/dx)` for the given function:

(cos x)^y = (cos y)^x

Find `bb(dy/dx)` for the given function:

xy = `e^((x - y))`

Find the derivative of the function given by f(x) = (1 + x) (1 + x²) (1 + x⁴) (1 + x⁸) and hence find f′(1).

Differentiate (x² – 5x + 8) (x³ + 7x + 9) in three ways mentioned below:

1. By using the product rule.
2. By expanding the product to obtain a single polynomial.
3. By logarithmic differentiation.

Do they all give the same answer?

If u, v and w are functions of x, then show that `d/dx(u.v.w) = (du)/dx v.w + u. (dv)/dx.w + u.v. (dw)/dx` in two ways-first by repeated application of product rule, second by logarithmic differentiation.