Differentiating fractional powers

CalculusAdditional / Further Maths

Apply the power rule to simple fractional powers on a stated domain.

Rewrite roots as powers, for example .
Use , keeping the fractional power exact.
These questions use , where every displayed fractional power is real and differentiable.

Example 1

Differentiate with respect to . Work on .

The power rule also works for these fractional powers.

Differentiate with respect to . Work on .

The power rule also works for these fractional powers.

Remember
Some original functions extend to or to negative inputs. The derivative formula must still be checked on the relevant local domain.

Question 1

Differentiate with respect to . Work on .

Check answer

The power rule also works for these fractional powers.

Question 2

Differentiate with respect to . Work on .

Check answer

The power rule also works for these fractional powers.

Question 3

Differentiate with respect to . Work on .

Check answer

The power rule also works for these fractional powers.

Question 4

Differentiate with respect to . Work on .

Check answer

The power rule also works for these fractional powers.

Question 5

Differentiate with respect to . Work on .

Check answer

The power rule also works for these fractional powers.