e^(x)sin x+x^(log8x)

Find the derivative of f(x)=log_(x)sin x^2 + (sin x^2) ^(log_ex) w.r.t. phi(x)= log_(e)x

Differentiate the following with respect to x:x^(3)e^(x)sin x (ii) x sin x log x (iii) x^(n)log_(a)xe^(x)

"If "f(x)=lim_(hrarr0) ((sin(x+h))^(log_(e)(x+h))-(sin x)^(log_(e)x))/(h)" then find "f(pi//2).

"If "f(x)=lim_(hrarr0) ((sin(x+h))^(log_(e)(x+h))-(sin x)^(log_(e)x))/(h)" then find "f(pi//2).

"If "f(x)=lim_(hrarr0) ((sin(x+h))^(log_(e)(x+h))-(sin x)^(log_(e)x))/(h)" then find "f(pi//2).

Find the derivative of 5 sin x + e^(x) log x .

int (sin x + cos x)/( e^(-x) + sin x) dx is equal to a) log | 1-e^(x) sin x| +C b) log | 1 + e^(-x) sin x| + C c) log | 1+e^(x) sin x| + C d) log | 1 -e^(-x) sinx | +C

int(1)/(1+tan x)dx=(log)_(e)(x+sin x)+C(b)(log)_(e)(sin x+cos x)+C(c)2(sec^(2)x)/(2)+C(d)(1)/(2){x+log(sin x+cos x)}+C

Which pair of functions is identical?a) sin^(-1)(sin x) and sin (sin^(-1)x) b) log_(e)e^(x),e^(log_ex) c) log_(e)x^2,2log_ex d)None of these