# Test: Differentiation - Ambitious

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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 $y=5{x}^{3}-2{x}^{2}+7x-15$
$\frac{dy}{dx}=125{x}^{2}-4x+49$
$\frac{dy}{dx}=-{x}^{2}+x-1$
$\frac{dy}{dx}=15{x}^{3}-4{x}^{2}+7x-15$
$\frac{dy}{dx}=15{x}^{2}-4x+7$
Question 3:   Find $\frac{{d}^{2}y}{d{x}^{2}}$ for $y=4{x}^{4}-3{x}^{3}-6{x}^{2}+x$
$\frac{{d}^{2}y}{d{x}^{2}}=48{x}^{2}-18x-12$
$\frac{{d}^{2}y}{d{x}^{2}}=16{x}^{2}-9x-12$
$\frac{{d}^{2}y}{d{x}^{2}}=8{x}^{2}-6x-8$
$\frac{{d}^{2}y}{d{x}^{2}}=16{x}^{3}-9{x}^{2}-12x+1$
Question 4:   Find $\frac{dy}{dx}$ at $x=3$ for $y=\frac{1}{2}{x}^{4}-\frac{3}{4}{x}^{3}+17$
$\frac{dy}{dx}=33.75$
$\frac{dy}{dx}=18$
$\frac{dy}{dx}=27.125$
$\frac{dy}{dx}=23.25$
Question 5:   Find $\frac{dy}{dx}$ of $y={e}^{x}\mathrm{cos}x$
$\frac{dy}{dx}=-{e}^{x}\left(\mathrm{cos}x-\mathrm{sin}x\right)$
$\frac{dy}{dx}={e}^{x}\left(\mathrm{cos}x-\mathrm{sin}x\right)$
$\frac{dy}{dx}={e}^{x}\left(\mathrm{sin}x-\mathrm{cos}x\right)$
$\frac{dy}{dx}=\mathrm{cos}x-\mathrm{sin}x$
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