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

Find the n^th derivative of the following:

`(1)/x`

Find the n^th derivative of the following : e^ax+b 

Find the nth derivative of the following : a^px+q 

Find the n^th derivative of the following : cos x

Find the n^th derivative of the following : sin (ax + b)

Find the n^th derivative of the following : cos (3 – 2x)

Find the n^th derivative of the following : `(1)/(3x - 5)`

Find the n^th derivative of the following : y = e^ax . cos (bx + c)

Find the n^th derivative of the following:

y = e^8x . cos (6x + 7)

Choose the correct option from the given alternatives : 

Let `f(1) = 3, f'(1) = -(1)/(3), g(1) = -4 and g'(1) =-(8)/(3).` The derivative of `sqrt([f(x)]^2 + [g(x)]^2` w.r.t. x at x = 1 is 

Choose the correct option from the given alternatives :

If y = sec (tan ^–1x), then `"dy"/"dx"` at x = 1, is equal to

Choose the correct option from the given alternatives :

If f(x) = `sin^-1((4^(x + 1/2))/(1 + 2^(4x)))`, which of the following is not the derivative of f(x)?

Choose the correct option from the given alternatives :

If y = sin (2sin^–1 x), then _dx = ........

Choose the correct option from the given alternatives :

If y = `tan^-1(x/(1 + sqrt(1 - x^2))) + sin[2tan^-1(sqrt((1 - x)/(1 + x)))] "then" "dy"/"dx"` = ...........

Choose the correct option from the given alternatives :

If `xsqrt(y + 1) + ysqrt(x + 1) = 0 and x ≠ y, "then" "dy"/"dx"` = ........

If y `tan^-1(sqrt((a - x)/(a +  x)))`, where – a < x < a, then `"dy"/"dx"` = .........

Choose the correct option from the given alternatives :

If x = a(cosθ + θ sinθ), y = a(sinθ – θ cosθ), then `((d^2y)/dx^2)_(θ = pi/4)` = .........

Choose the correct option from the given alternatives :

If y = `a cos (logx) and "A"(d^2y)/(dx^2) + "B""dy"/"dx" + "C"` = 0, then the values of A, B, C are

Solve the following : 

f(x) = –x, for – 2 ≤ x < 0
= 2x, for 0 ≤ x < 2
= `(18 - x)/(4)`, for 2 < x ≤ 7
g(x) = 6 – 3x, for 0 ≤ x < 2
= `(2x - 4)/(3)`, for 2 < x ≤ 7
Let u (x) = f[g(x)], v(x) = g[f(x)] and w(x) = g[g(x)]. Find each derivative at x = 1, if it exists i.e. find u'(1), v' (1) and w'(1). If it doesn't exist, then explain why?

Suppose that the functions f and g and their derivatives with respect to x have the following values at x = 0 and x = 1: 

(i) The derivative of f[g(x)] w.r.t. x at x = 0 is ......
(ii) The derivative of g[f(x)] w.r.t. x at x = 0 is ......
(iii) The value of `["d"/"dx"[x^(10) + f(x)]^(-2)]_(x = 1_` is ........
(iv) The derivative of f[(x + g(x))] w.r.t. x at x = 0 is ...