HSC Science (General) 12th Standard Board Exam - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Differentiate the following w.r.t. x : (sin x)^x 

Differentiate the following w.r.t. x: (sin x^x)

Differentiate the following w.r.t. x: x^e + x^x + e^x + e^e.

Differentiate the following w.r.t. x:

`x^(x^x) + e^(x^x)`

Differentiate the following w.r.t. x : (logx)^x – (cos x)^cotx 

Differentiate the following w.r.t. x : `x^(e^x) + (logx)^(sinx)`

Differentiate the following w.r.t. x :

e^tanx + (logx)^tanx 

Differentiate the following w.r.t. x :

(sin x)^tanx + (cos x)^cotx 

Differentiate the following w.r.t. x : `10^(x^(x)) + x^(x(10)) + x^(10x)`

Differentiate the following w.r.t. x : `[(tanx)^(tanx)]^(tanx) "at"  x = pi/(4)`

Show that `"dy"/"dx" = y/x` in the following, where a and p are constants : x⁷.y⁵ = (x + y)¹² 

Show that `bb("dy"/"dx" = y/x)` in the following, where a and p are constant:

x^py⁴ = (x + y)^p+4, p ∈ N

Show that `"dy"/"dx" = y/x` in the following, where a and p are constants : `sec((x^5 + y^5)/(x^5 - y^5))` = a² 

Show that `"dy"/"dx" = y/x` in the following, where a and p are constants : `tan^-1((3x^2 - 4y^2)/(3x^2 + 4y^2))` = a² 

Show that `"dy"/"dx" = y/x` in the following, where a and p are constants : `cos^-1((7x^4 + 5y^4)/(7x^4 - 5y^4)) = tan^-1a`

Show that `"dy"/"dx" = y/x` in the following, where a and p are constants: `log((x^20 - y^20)/(x^20 + y^20))` = 20

Show that `"dy"/"dx" = y/x` in the following, where a and p are constants : `e^((x^7 - y^7)/(x^7 + y^7)` = a

Show that `"dy"/"dx" = y/x` in the following, where a and p are constants : `sin((x^3 - y^3)/(x^3 + y^3))` = a³ 

If y is a function of x and log (x + y) = 2xy, then the value of y'(0) = ______.

Solve the following : 

The values of f(x), g(x), f'(x) and g'(x) are given in the following table :

Match the following :