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These are the Transum resources related to the statement: "Differentiate x^{n}, for rational values of n, and related constant multiples, sums and differences. Differentiate e^{kx} and a^{kx}, sin kx, cos kx, tan kx and related sums, differences and constant multiples. Understand and use the derivative of ln x".

Here are some exam-style questions on this statement:

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*A function is given as \(f(x)=3x^2-6x+4+\frac3x,-2\le x \le 4, x\ne 0\).*" ... more - "
*Consider the graph of the function \(f(x)=7-3x^2-x^3\)*" ... more - "
*A package is in the shape of a cuboid and has a length \(l\) cm, width \(w\) cm and height of 12 cm.*" ... more - "
*Let \(f(x)=\frac{2x}{x^2+3}\)*" ... more - "
*Consider the function \(f(x)=6 - ax+\frac 3{x^2},x\neq 0\)*" ... more - "
*Consider the function \(f\) defined by \(f(x)= \ln{(x^2 - 9)}\) for \(x > 3\).*" ... more - "
*If \(f(x)=x\sin{x}\), for \(-3\le x\le3\)*" ... more - "
*Consider the cubic function \(f(x)=\frac{1}{6}x^3-2x^2+6x-2\)*" ... more - "
*Consider the function \(f(x)=x^3-9x+2\).*" ... more - "
*The displacement, in millimetres, of a particle from an origin, O, at time t seconds, is given by \(s(t) = t^3 cos t + 5t sin t\) where \( 0 \le t \le 5 \) .*" ... more - "
*The function \(f\) is defined as follows:*" ... more - "
*Consider the functions*" ... more - "
*Let \(f(x)=jx^3+jx^2+kx+m\) where \(j, k\) and \(m\) are constants.*" ... more - "
*Make a sketch of a graph showing the velocity (in \(ms^{-1}\)) against time of a particle travelling for six seconds according to the equation:*" ... more - "
*Let \(f(x) = \frac{ln3x}{kx} \) where \( x \gt 0\) and \( k \in \mathbf Q^+ \).*" ... more - "
*The function \(f\) is such that \(f(x) = \frac{\ln2x}{x^3} \) where \(x \gt 0\).*" ... more - "
*Consider the function \(f\) defined by \(f(x) = 25e^{x-5}\) for \(x \in \mathbb{R}^+\).*" ... more - "
*Consider the function \(f(x)=\frac{20}{x^2}+kx\) where \(k\) is a constant and \(x\neq0\).*" ... more

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