Differentiation questions | form five Pure Advanced Mathematics

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

#	Question
1	Find the relative maximum and relative minimum values of the function $y=frac{x}{1+x^{2}}$ Mathematical Calculation
2	Use Taylor`s theorem to obtain a series expansion for $cos (x+frac{pi}{3})$ stating terms up to and including that in $x^{3}$ Find the minimum and maximum value of $3cosh,x+2Sinh,x$ Mathematical Calculation
3	If $xsqrt{(1+y)} =ysqrt{(1+x)}=0$ , prove that $frac{dy}{dx}=-frac{1}{(1+x)^2}$ Given that $f=sin ,xy$ find $frac{partial f}{partial x}$ and $frac{partial f}{partial y}$ Using Taylor`s theorem, expand $sin(frac{pi}{6}+h)$ in ascending power of h up to $h^{4}$ term and hence evaluate $sin 31^{circ}$ correct to three decimal places. Mathematical Calculation
4	If the minimum value of $f(x)=2x^{3}+3x^{2}-12x+k$ is one-tenth of its maximum value, find the value of k. Mathematical Calculation
5	If $f(x,y)=x^{3}y+e^{xy^{2}})$ , Find $frac{partial f }{partial x} , and , frac{partial f}{partial y}$ . If $z=x^{2} an^{-1}left ( frac{y}{x} ight )$ , find $frac{partial^2 z }{partial x partial y}$ at (1,1). Mathematical Calculation
6	Differentiate $cosh^{6}x$ with respect to x. Mathematical Calculation
7	Given the curve $xsin y +ycos x=2$ . Find $frac{mathrm{d}y }{mathrm{d} x}$ when $x=frac{pi}{2}$ and $y=pi$ . Mathematical Calculation
8	Use the second derivative test to investigate the stationary values of the function $f(x)=2x^{2}-8x+5$ . Mathematical Calculation
9	Differentiate $f(x)=frac{1}{2}cos 3x$ from first principles. Mathematical Calculation
10	If $xsqrt{1+y}+ysqrt{1+x}=0$ , prove that $frac{dy}{dx}=-frac{1}{(1+x)^{2}}$ Mathematical Calculation