Differentiation questions | form five Pure Advanced Mathematics

Find Differentiation examination questions, form five Pure Advanced Mathematics in acaproso.com

#	Question
1	Differentiate from the first principles the function $y=frac{2}{1+x^{2}}$ If $y=sqrt{frac{1+sin,x}{1-sin,x}}$ , show that $frac{dy}{dx}=frac{1}{1-sin,x}$ Mathematical Calculation
2	Differentiate with respect to x $lnfrac{(1+sin,x)}{1+sin,2x}$ $cot(3x^{2}+2)$ Mathematical Calculation
3	Find the derivative of $y=x^{sin,x}$ Mathematical Calculation
4	Differentiate $log_{10}x^{2}$ $tan^{-1}(coth,x)$ $lnfrac{sin,x}{cos,2x}$ Mathematical Calculation
5	Given the curve $y^{2}+2xy-3x^{2}-5=0$ . Find the values of $frac{d^{2}y}{dx^{2}}$ at the point where x=1 and y has a positive value. Differentiate with respect to x given that $y=(x^2+1)^{sin.x}$ Mathematical Calculation
6	Find $frac{dy}{dx}$ and simplify your answer given that $y=frac{e^x-1}{e^x+1}$ Mathematical Calculation
7	Find $frac{dy}{dx}$ if $e^{xy}+x+y=1$ $tanh^{-1}frac{2x}{1+x^2}$ Mathematical Calculation
8	An error of 2% is made in measuring the radius of a sphere. What is the resulting percentage error in the calculation of its surface area?. Mathematical Calculation
9	If $ln (x+y)=tan^{-1}(frac{x}{y})$ find $frac{dy}{dx}$ The pressure p and the volume v of an expanding gas are related by $pv^{1.4}=k.$ If the volume increases by 0.3%, what is the corresponding percentage change in the pressure? Mathematical Calculation
10	If $R=ar^{n}$ where “a” is a constant and an error of x% is made in measuring r, prove that the resulting error in R is nx%. A curve is defined by parametric equations $x=frac{t}{1+t^{2}}$ and $y=frac{1}{(t-1)}$ . Find $frac{d^2y}{dx^2}$ Mathematical Calculation