MathsQuestions

Find $\dfrac{\mathrm{d}y}{\mathrm{d}x}$ given that $$y = \mathrm{e}^{3x}$$

$3\mathrm{e}^{3x}$

Find $\dfrac{\mathrm{d}y}{\mathrm{d}x}$ given that $$y = \sin(5x)$$

$5\cos(5x)$

Find $\dfrac{\mathrm{d}y}{\mathrm{d}x}$ given that $$y = \ln(2x + 1)$$

$\dfrac{2}{2x + 1}$

Find $\dfrac{\mathrm{d}y}{\mathrm{d}x}$ given that $$y = \cos(x^2)$$

$-2x\sin(x^2)$

Find $\dfrac{\mathrm{d}y}{\mathrm{d}x}$ given that $$y = \mathrm{e}^{x^2}$$

$2x\,\mathrm{e}^{x^2}$

Find $\dfrac{\mathrm{d}y}{\mathrm{d}x}$ given that $$y = \ln(\cos x)$$

$-\tan x$

Find $\dfrac{\mathrm{d}y}{\mathrm{d}x}$ given that $$y = \mathrm{e}^{\sin x}$$

$\cos x \, \mathrm{e}^{\sin x}$

Find $\dfrac{\mathrm{d}y}{\mathrm{d}x}$ given that $$y = \sin^2(3x)$$

$6\sin(3x)\cos(3x)$

Find $\dfrac{\mathrm{d}y}{\mathrm{d}x}$ given that $$y = x \mathrm{e}^{x}$$

$\mathrm{e}^{x}(1 + x)$

Find $\dfrac{\mathrm{d}y}{\mathrm{d}x}$ given that $$y = x^2 \sin x$$

$2x\sin x + x^2\cos x$

Find $\dfrac{\mathrm{d}y}{\mathrm{d}x}$ given that $$y = \mathrm{e}^{x}\cos x$$

$\mathrm{e}^{x}(\cos x - \sin x)$

Find $\dfrac{\mathrm{d}y}{\mathrm{d}x}$ given that $$y = x \ln x$$

$\ln x + 1$

Find $\dfrac{\mathrm{d}y}{\mathrm{d}x}$ given that $$y = \mathrm{e}^{2x}\sin x$$

$\mathrm{e}^{2x}(2\sin x + \cos x)$

Find $\dfrac{\mathrm{d}y}{\mathrm{d}x}$ given that $$y = x^2 \ln x$$

$2x\ln x + x$

Find $\dfrac{\mathrm{d}y}{\mathrm{d}x}$ given that $$y = \sin x \cos x$$

$\cos^2 x - \sin^2 x$

Find $\dfrac{\mathrm{d}y}{\mathrm{d}x}$ given that $$y = \dfrac{\sin x}{x}$$

$\dfrac{x\cos x - \sin x}{x^2}$

Find $\dfrac{\mathrm{d}y}{\mathrm{d}x}$ given that $$y = \dfrac{\mathrm{e}^{x}}{x}$$

$\dfrac{\mathrm{e}^{x}(x - 1)}{x^2}$

Find $\dfrac{\mathrm{d}y}{\mathrm{d}x}$ given that $$y = \dfrac{x}{\mathrm{e}^{x}}$$

$\dfrac{1 - x}{\mathrm{e}^{x}}$

Find $\dfrac{\mathrm{d}y}{\mathrm{d}x}$ given that $$y = \dfrac{\ln x}{x}$$

$\dfrac{1 - \ln x}{x^2}$

Find $\dfrac{\mathrm{d}y}{\mathrm{d}x}$ given that $$y = \dfrac{\sin x}{\cos x}$$

$\dfrac{1}{\cos^2 x}$

Find $\dfrac{\mathrm{d}y}{\mathrm{d}x}$ given that $$y = \dfrac{x^2}{\sin x}$$

$\dfrac{2x\sin x - x^2\cos x}{\sin^2 x}$

Find $\dfrac{\mathrm{d}y}{\mathrm{d}x}$ given that $$y = \dfrac{\mathrm{e}^{x}}{x + 1}$$

$\dfrac{x \mathrm{e}^{x}}{(x + 1)^2}$

Find the equation of the tangent to the curve $$y = \mathrm{e}^{x}$$ at the point $(0, 1)$.

$y = x + 1$

Find the equation of the tangent to the curve $$y = \ln x$$ at the point $(1, 0)$.

$y = x - 1$

Find the equation of the normal to the curve $$y = \mathrm{e}^{2x}$$ at the point $(0, 1)$.

$y = 1 - \dfrac{1}{2}x$

Find the equation of the tangent to the curve $$y = \sin x$$ at the point $(0, 0)$.

$y = x$

Find the equation of the tangent to the curve $$y = \cos x$$ at the point $\left(\dfrac{\pi}{2}, 0\right)$.

$y = -x + \dfrac{\pi}{2}$

Find the equation of the normal to the curve $$y = \ln x$$ at the point $(1, 0)$.

$y = 1 - x$

Find the equation of the tangent to the curve $$y = x \mathrm{e}^{x}$$ at the point $(1, \mathrm{e})$.

$y = 2\mathrm{e}x - \mathrm{e}$

Find the equation of the normal to the curve $$y = x^2 \mathrm{e}^{x}$$ at the point $(0, 0)$.

$x = 0$