List of practice Questions

Find \(\frac{dy}{dx}\) of function
\(xy=e^{(x-y)}\)

Find \(\frac{dy}{dx}\) of function
\((cosx)^y=(cosy)^x\)

Find \(\frac{dy}{dx}\) of function
\(y^x=x^y\)

Find \(\frac{dy}{dx}\) of function
\(x^y+y^x=1\)

Differentiate the function with respect to \(x\)
\((xcosx)^x+(xsinx)^{\frac{1}{x}}\)

Differentiate the function with respect to \(x\)
\(x^{xcos\,x}+\frac{x^2+1}{x^2-1}\)

Differentiate the function with respect to \(x\):
\(x^{sin\,x}+(sin\,x)^{cos\,x}\)

Differentiate the function with respect to \(x\):
\((sin\,x)^x+sin^{-1}\sqrt{x}\)

Differentiate the function with respect to \(x\)
\((log\,x)^x+x^{log\,x}\)

Differentiate the function with respect to \(x\). 
\((x+\frac{1}{x})^x+x^{(1+\frac{1}{x})}\)

Differentiate the function with respect to \(x\). 
\((x+3)^2.(x+4)^3.(x+5)^4\)

Differentiate the function with respect to \(x\). 
\(x^x-2^{sinx}\)

Differentiate the following w.r.t. \(x\):\((log\,x)^{cos\,x}\)

Differentiate the following w.r.t. \(x\):
\(\sqrt{\frac{(x-1)(x-2)}{(x-3)(x-4)(x-5)}}\)

Differentiate the following w.r.t. \(x\):
\(cos(log\,x+e^x),x>0\)

Differentiate the following w.r.t. \(x\):
\(\frac{cos\,x}{log\,x},x>0\)

Differentiate the following w.r.t. \(x\):
\(log(log\,x),x>1\)

Differentiate the following w.r.t. \(x\):
\(\sqrt{e^{\sqrt{x}}},x>0\)

Differentiate the following w.r.t. \(x\):
\(e^x+e^{x^2}+....+e^{x^5}\)

Differentiate the following w.r.t. \(x\):
\(log(cos\,e^x)\)

Differentiate the following w.r.t. \(x\):
\(sin(tan^{-1}e^{-x})\)

A steel wire of length $l$ has a magnetic moment $M$. It is then bent into a semicircular arc. The new magnetic moment is

Find the intervals in which the function \(f\) given by \(f(x) = 2x^2 − 3x\) is (a) strictly increasing (b) strictly decreasing

Show that the function given by \(f(x) = sin x\) is (a) strictly increasing in \((0,\frac{π}{2})\) (b) strictly decreasing in \((\frac{π}{2},π)\) (c) neither increasing nor decreasing in \((0, π)\)

Show that the function given by \(f(x) = e^{2x}\) is strictly increasing on \(R\).