Find the gradient of the curve $y = x^{4} (2 x - 1)$ at $x = 1$ .

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Find the derivative of $y = \frac{l n x}{x ^{2}}$ with respect to $x$ for $x > 0$ .
The equation of a curve is $y = 2 x^{3} - 9 x^{2} + 12 x + 5$ . Find the coordinates of the stationary points and determine their nature.
A spherical balloon is being inflated so that its volume increases at a constant rate of $36 π cm^{3} / s$ . Find the rate of incr…
Find the equation of the normal to the curve $y = 3 e^{2 x} - 1$ at the point where $x = 0$ .
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A piece of wire of length $40 cm$ is bent into the shape of a sector of a circle of radius $r cm$ and angle $θ$ radians.…