Derivative of a fractional power function

Let $f(x) = x^{0.75}$ . Find $f'(x)$ .

Hint

Apply the power rule $\frac{d}{dx}[x^n] = n x^{n-1}$ directly with $n = 0.75$ .

Step-by-step solution

Using the power rule, bring the exponent $0.75$ down as a coefficient: $f'(x) = 0.75 \cdot x^{0.75 - 1}$ .

Simplify the exponent: $0.75 - 1 = -0.25$ , so $f'(x) = 0.75\, x^{-0.25}$ , which can also be written as $\dfrac{3}{4\,x^{0.25}}$ .

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