11. Differentiation

iGCSE (2021 Edition)

Determine the derivative of $y=x^{\frac{6}{5}}$`y`=`x`65.

Easy

< 1min

Determine the derivative of $y=x^{0.6}$`y`=`x`0.6.

Easy

< 1min

Differentiate $y=x^{-\frac{1}{5}}$`y`=`x`−15 with respect to $x$`x`. Express your answer in positive index form.

Easy

2min

Find the derivative of $y=x-x^3+\sqrt[8]{x}+3$`y`=`x`−`x`3+^{8}√`x`+3.

Give your answer with positive indices.

Easy

2min

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Use the notations f'(x), f''(x), dy/dx, d^2y/dx^2 [=d/dx(dy/dx)].

Use the derivatives of the standard functions x^n (for any rational n), together with constant multiples, sums and composite functions.