# Test: Differentiation - Ambitious

Double click on maths expressions to zoom
Question 1:   Find the gradient of a straight line whith the points $P\left(5,3\right)$ and $Q\left(8,12\right)$
$1$
$-1$
$3$
$2$
Question 2:   Find $\frac{dy}{dx}$for $y=5{x}^{3}-2{x}^{2}+7x-15$
$\frac{dy}{dx}=15{x}^{3}-4{x}^{2}+7x-15$
$\frac{dy}{dx}=-{x}^{2}+x-1$
$\frac{dy}{dx}=15{x}^{2}-4x+7$
$\frac{dy}{dx}=125{x}^{2}-4x+49$
Question 3:   Find $\frac{{d}^{2}y}{d{x}^{2}}$ for $y=4{x}^{4}-3{x}^{3}-6{x}^{2}+x$
$\frac{{d}^{2}y}{d{x}^{2}}=16{x}^{3}-9{x}^{2}-12x+1$
$\frac{{d}^{2}y}{d{x}^{2}}=16{x}^{2}-9x-12$
$\frac{{d}^{2}y}{d{x}^{2}}=8{x}^{2}-6x-8$
$\frac{{d}^{2}y}{d{x}^{2}}=48{x}^{2}-18x-12$
Question 4:   Find $\frac{dy}{dx}$ at $x=3$ for $y=\frac{1}{2}{x}^{4}-\frac{3}{4}{x}^{3}+17$
$\frac{dy}{dx}=33.75$
$\frac{dy}{dx}=27.125$
$\frac{dy}{dx}=18$
$\frac{dy}{dx}=23.25$
Question 5:   Find $\frac{dy}{dx}$ of $y={e}^{x}\mathrm{cos}x$
$\frac{dy}{dx}=-{e}^{x}\left(\mathrm{cos}x-\mathrm{sin}x\right)$
$\frac{dy}{dx}=\mathrm{cos}x-\mathrm{sin}x$
$\frac{dy}{dx}={e}^{x}\left(\mathrm{cos}x-\mathrm{sin}x\right)$
$\frac{dy}{dx}={e}^{x}\left(\mathrm{sin}x-\mathrm{cos}x\right)$
Question 6:   Find $\frac{dy}{dx}$ of $y=7{x}^{4}\mathrm{sin}x$
$\frac{dy}{dx}={x}^{3}\left(7x\mathrm{cos}x+\mathrm{sin}x\right)$
$\frac{dy}{dx}=7{x}^{4}\left(\mathrm{cos}x+4\mathrm{sin}x\right)$
$\frac{dy}{dx}=21{x}^{2}\left(x\mathrm{cos}x-4\mathrm{sin}x\right)$
$\frac{dy}{dx}=7{x}^{3}\left(x\mathrm{cos}x+4\mathrm{sin}x\right)$
Question 7:   Find $\frac{dy}{dx}$ of $y=\frac{\mathrm{sin}x}{{x}^{5}}$
$\frac{dy}{dx}=5\frac{\mathrm{cos}x}{{x}^{4}}$
$\frac{dy}{dx}=\frac{5\mathrm{cos}x-x\mathrm{sin}x}{{x}^{5}}$
$\frac{dy}{dx}=5\frac{\mathrm{cos}x-\mathrm{sin}x}{{x}^{4}}$
$\frac{dy}{dx}=\frac{x\mathrm{cos}x-5\mathrm{sin}x}{{x}^{6}}$
Question 8:   Find $\frac{dy}{dx}$ of $y=\frac{{e}^{x}}{\mathrm{tan}x}$
$\frac{dy}{dx}=\frac{{e}^{x}\left(\mathrm{tan}x-{\mathrm{sec}}^{2}x\right)}{{\mathrm{tan}}^{2}x}$
$\frac{dy}{dx}=\frac{{e}^{x}}{{\mathrm{sec}}^{2}x}$
$\frac{dy}{dx}=\frac{{e}^{x}}{\mathrm{sec}x}$
$\frac{dy}{dx}=\frac{{e}^{x}\left(\mathrm{sin}x-\mathrm{cos}x\right)}{{\mathrm{tan}}^{2}x}$
Question 9:   Find $\frac{dy}{dx}$ of $y={\left(2x+7\right)}^{5}$
$\frac{dy}{dx}=5{\left(2x+7\right)}^{4}$
$\frac{dy}{dx}=10{\left(2x+7\right)}^{4}$
$\frac{dy}{dx}={\left(2x+7\right)}^{4}$
$\frac{dy}{dx}=15{x}^{4}$
Question 10:   Find $\frac{dy}{dx}$ of $y=6{e}^{\mathrm{cos}x}$
$\frac{dy}{dx}=6\mathrm{cos}x{e}^{\mathrm{cos}x}$
$\frac{dy}{dx}=-6\mathrm{sin}{e}^{\mathrm{cos}x}$
$\frac{dy}{dx}=-6\mathrm{cos}{e}^{\mathrm{sin}x}$
$\frac{dy}{dx}=-6\mathrm{sin}x{e}^{\mathrm{cos}x}$