The gradient of the tangent to the curve $y = lo g_{e} (x^{2} + 1)$ at $x = 1$ is:

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If $y = e^{2 x} sin (3 x)$ , then $\frac{d y}{d x}$ is equal to:
A cylindrical can with an open top has a fixed volume of $128 π cm^{3}$ . Find the radius $r$ that minimises the total exterior surface…
Find the coordinates of the inflection point of the cubic function $f (x) = 2 x^{3} - 6 x^{2} + 5 x - 3$ .
The tangent line to the curve $y = x^{3} - a x + 2$ at $x = 1$ is parallel to the line $y = 5 x - 4$ . Find the value of $a$ .
Let $f (x) = k x - sin (2 x)$ . Find the set of all real values of $k$ for which $f (x)$ is strictly increasing on $R$ .
Find $\frac{d y}{d x}$ when $y = \frac{lo g _{e} ( x )}{x}$ .