Define h(x)= (x^ 2 +1) x x + (3x-2) x x^ 2

MATHEMATICS · Subjective · A Level · Mathematics · Differentiation · Differentiation

Problem

Define h(x)=(x2+1)cos⁡xx+(3x−2)sin⁡xx2.h(x)=\frac{(x^{2}+1)\cos x}{x}+\frac{(3x-2)\sin x}{x^{2}}. (i) Differentiate h(x)h(x) with respect to xx. (ii) Show that your result can be arranged in the form h′(x)=(1+3x−3x2)cos⁡x+(−x−1x−3x2+4x3)sin⁡x.h'(x)=\left(1+\frac{3}{x}-\frac{3}{x^{2}}\right)\cos x+\left(-x-\frac{1}{x}-\frac{3}{x^{2}}+\frac{4}{x^{3}}\right)\sin x.

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