Differentiating standard functionsEdexcel A-Level Maths: Mind map

Exam questions on Differentiating standard functions

1. A curve has equation $y=e^{3x}+\sin 2x$, where $x$ is in radians.
   Find the equation of the tangent to the curve at the point where $x=0$.2 marks
2. The function $f$ is defined by $f(x)=5^{2x}$ for all real $x$.
   Find the exact value of $x$ for which $f'(x)=50\ln5$.2 marks
3. The curve $y=\sin x$ (with $x$ in radians) has a point $P$ with $x$-coordinate $x$. A point $Q$ on the curve has $x$-coordinate $x+h$, where $h$ is small and non-zero.
   Show that the gradient of the chord $PQ$ is $\sin x\left(\frac{\cos h-1}{h}\right)+\cos x\left(\frac{\sin h}{h}\right)$.3 marks