a^(x)-2^(sin x)

If f(x)=2^(sin x) then f'(x)=

Prove that: ,,(sin x-sin3x)/(sin^(2)x-cos^(2)x)=2sin x

lim_(x rarr0)(2+2x+sin2x)/((2x+sin2x)e^(sin x)) is

lim_ (x rarr oo) (2 + 2x + sin2x) / ((2x + sin2x) e ^ (sin x)) is:

The range of the function f(x)=sgn((sin^(2)x+2sin x+4)/(sin^(2)x+2sin x+3)) is

Ascertain the existence of the following limits : lim_(xtooo) (2+2x+sin 2x)/((2x+sin 2x)e^(sin x))

int_( equal to )^((x-sin x)^((3)/(2))){(6x^(2)sin^(2)((x)/(2)))/(x-sin x)+3x}dx is

((1) / ((sec x) ^ (2) - (cos x) ^ (2)) + (1) / ((cos ecx) ^ (2) - (sin x) ^ (2))) ( cos x) ^ (2) (sin x) ^ (2) = (1- (cos x) ^ (2) (sin x) ^ (2)) / (2+ (cos x) ^ (2) (sin x) ^ (2))

Prove that (sin x-sin 3 x)/(sin ^(2) x-cos ^(2) x)=2 sin x

Evaluate int (sin x cos x)/(sin^2x- 2sin x+3) dx