Practice sheet

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$f(x) = 8x^{ 5 } + 3x$ . Find $f'(x)$ .
$f(x) = \dfrac{ 6 }{x^{ 2 } }$ . Find $f'(x)$ .
$f(x) = 3\sqrt{x} + 8$ . Find $f'(x)$ .
$f(x) = 8e^x + 5x^2$ . Find $f'(x)$ .
$f(x) = 3^x$ . Find $f'(x)$ .
Find the slope of the tangent line to $y = 8e^x + 1$ at $x = 0$ .
$f(x) = 3\sin x + 5\cos x$ . Find $f'(x)$ .
Find the slope of the tangent line to $y = \sin x$ at $x = \dfrac{\pi}{ 2 }$ . Give an exact value.
$f(x) = 4x - 4\cos x$ . Find $f'(x)$ .
$f(x) = x^{ 2 }\sin x$ . Find $f'(x)$ .
$f(x) = (x + 3)e^x$ . Find $f'(x)$ .
$f(2) = 4$ , $f'(2) = 4$ , $g(2) = -4$ and $g'(2) = -1$ . Find $(fg)'(2)$ .
$f(x) = \dfrac{x}{x + 6}$ . Find $f'(x)$ .
$f(x) = \dfrac{ 4\sin x}{x}$ . Find $f'(x)$ .
$f(1) = 1$ , $f'(1) = -2$ , $g(1) = 4$ and $g'(1) = 2$ . Find $\left(\dfrac{f}{g}\right)'(1)$ .
$f(x) = 7\tan x$ . Find $f'(x)$ .
$f(x) = \sec x + 2\cot x$ . Find $f'(x)$ .
Find the slope of the tangent line to $y = \tan x$ at $x = \dfrac{\pi}{ 6 }$ . Give an exact value.
$f(x) = (6x + 7)^{ 4 }$ . Find $f'(x)$ .
$f(x) = \sin(4x^2)$ . Find $f'(x)$ .
$f(x) = e^{ 5x^2}$ . Find $f'(x)$ .
$f(x) = \ln(9x)$ for $x > 0$ . Find $f'(x)$ .
$f(x) = \ln(x^2 + 2)$ . Find $f'(x)$ .
$f(x) = \arctan(7x)$ . Find $f'(x)$ .

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