List of practice Questions

Which of the following is an antihistamine drug?

If \(x\) and \(y\) are connected parametrically by the equation,without eliminating the parameter,find \(\frac{dy}{dx}\).
\(x=4t,y=\frac{4}{t}\)

If \(x\) and \(y\) are connected parametrically by the equation,without eliminating the parameter,find \(\frac{dy}{dx}\).
\(x=sin\,t,y=cos\,2t\)

If \(x\) and \(y\) are connected parametrically by the equation,without eliminating the parameter,find \(\frac{dy}{dx}\).
\(x= a\,cos\,θ,y=b\,cos\,θ\)

If \(x\) and \(y\) are connected parametrically by the equation,without eliminating the parameter,find \(\frac{dy}{dx}.\)
\(x=2at^2,y=at^4\)

If \(u,v\) and \(w\) are functions of \(x\),then show that
\(\frac{d}{dx}(u.v.w)=\frac{du}{dx}v.w+u.\frac{dv}{dx}+u.v\frac{dw}{dx}\) in two ways-first by repeated application of product rule,second by logarithmic differentiation.

Find the derivative of the function given by \(f(x)=(1+x)(1+x^2)(1+x^4)(1+x^8)\) and hence find \(f'(1)\)

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. \(x\):
\(\sqrt{e^{\sqrt{x}}},x>0\)