# Test: Differentiation I - Normal

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Question 1:   Differentiate $y$ with respect to $x:$ $y={x}^{2}-5x$
$\frac{dy}{dx}={x}^{2}-5$
$\frac{dy}{dx}=-5$
$\frac{dy}{dx}=2x-5$
$\frac{dy}{dx}=2x$
Question 2:   Differentiate $y$ with respect to $x:$ $y=\mathrm{ln}\left(x\right)$
$\frac{dy}{dx}=\frac{1}{{x}^{2}}$
$\frac{dy}{dx}=\mathrm{ln}\left(\frac{1}{x}\right)$
$\frac{dy}{dx}=\frac{1}{x}$
$\frac{dy}{dx}=\frac{1}{{x}^{2}+1}$
Question 3:   The function f is defined by: $f\left(x\right)=5$. Find $f\text{'}\left(x\right)$
$f\text{'}\left(x\right)=5$
$f\text{'}\left(x\right)=x$
$f\text{'}\left(x\right)=0$
$f\text{'}\left(x\right)=1$
Question 4:   Differentiate $y$ with respect to $x:$ $y=\mathrm{tan}\left(5x\right)$
$\frac{dx}{dy}=\frac{1}{{\mathrm{cos}}^{2}\left(5x\right)}$
$\frac{dx}{dy}=\frac{1}{{\mathrm{cos}}^{2}\left(x\right)}$
$\frac{dx}{dy}=\frac{5}{{\mathrm{cos}}^{2}\left(x\right)}$
$\frac{dx}{dy}=\frac{5}{{\mathrm{cos}}^{2}\left(5x\right)}$
Question 5:   Find the gradient of the function $y={x}^{3}$ at the point ${x}_{0}=2$
$k=0.5$
$k=8$
$k=12$
$k=4$
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