Prove that the curves `y=f(x),[f(x)>0],a n dy=f(x)sinx ,w h e r ef(x)` is differentiable function, have common tangents at common points.

Prove that the curves y=f(x),[f(x)>0], and y=f(x)sin x, where f(x) is differentiable function,have common tangents at common points.

Prove that the curves y_(1) = f (x) (f(x) gt 0) and y_(2) = f(x) sin x, where f(x) is a differentiable function, are tangent to each other at the common points.

f(x)=int_0^x e^t f(t)dt+e^x , f(x) is a differentiable function on x in R then f(x)=

A function f satisfies the condition f(x)=f^(prime)(x)+f''(x)+f'''(x)....+infinity ,w h e r ef(x) is a differentiable function indefinitely and dash denotes the order of derivative. If f(0)=1,t h e nf(x) is e^(x/2) (b) e^x (c) e^(2x) (d) e^(4x)

Let g(x)=f(x)sinx ,w h e r ef(x) is a twice differentiable function on (-oo,oo) such that f(-pi)=1. The value of |g^n (-pi)| equals __________

Let g(x)=f(x)sinx ,w h e r ef(x) is a twice differentiable function on (-oo,oo) such that f'(-pi)=1. The value of |g^''(-pi)| equals __________

Let g(x)=f(x)sinx ,w h e r ef(x) is a twice differentiable function on (-oo,oo) such that f'(-pi)=1. The value of |g^(-pi)| equals __________

Let g(x)=f(x)sinx ,w h e r ef(x) is a twice differentiable function on (-oo,oo) such that f'(-pi)=1. The value of g''(-pi) equals __________

Let g(x)=f(x)sinx ,w h e r ef(x) is a twice differentiable function on (-oo,oo) such that f(-pi)=1. The value of |g^''(-pi)| equals __________

If f is a differentiable function and 2f(sinx) + f(cosx)=x AA x in R then f'(x)=