Solve 4(x^3/4)^-5

$$4 ( x ^ { 3 / 4 } ) ^ { - 5 }$$

Differentiate w.r.t. x

$$-\frac{15}{x^{\frac{19}{4}}}$$

Steps Using Definition of a Derivative

To raise a power to another power, multiply the exponents. Multiply \frac{3}{4} and -5 to get -\frac{15}{4}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x^{-\frac{15}{4}})$$

The derivative of ax^{n} is nax^{n-1}.

$$-\frac{15}{4}\times 4x^{-\frac{15}{4}-1}$$

Multiply -\frac{15}{4} times 4.

$$-15x^{-\frac{15}{4}-1}$$

Subtract 1 from -\frac{15}{4}.

$$-15x^{-\frac{19}{4}}$$

Evaluate

$$\frac{4}{x^{\frac{15}{4}}}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply \frac{3}{4} and -5 to get -\frac{15}{4}.

$$4x^{-\frac{15}{4}}$$