Differentiate with respect to xxx: e3x(sinx+2cosx)e^{3x}(\sin x + 2 \cos x)e3x(sinx+2cosx).
Differentiate with respect to xxx: x3ln(5x+2)x^3 \ln (5x + 2)x3ln(5x+2).
Given that y=3x2+6x−7(x+1)2,x≠−1\displaystyle y = \frac{3x^2 + 6x - 7}{(x + 1)^2}, x \neq -1y=(x+1)23x2+6x−7,x=−1, show that dydx=20(x+1)3\displaystyle \frac{dy}{dx} = \frac{20}{(x + 1)^3}dxdy=(x+1)320.
Hence find d2ydx2\displaystyle \frac{d^2y}{dx^2}dx2d2y and the real values of x x\,x for which d2ydx2=−154\displaystyle \frac{d^2y}{dx^2} = -\frac{15}{4}dx2d2y=−415.
Practise Edexcel A Level Old Maths Differentiation with exam-style questions for A Level Old Maths. 14 questions, matched to the Edexcel A Level Old Maths (9371) specification and written in Unit exams C1, C2, C3 and C4 plus two applied units (e.g. S1 and M1) style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.