Solve 3/16*{x}^frac{4{5}-1}

$$\frac{ 3 }{ 16 } \times { x }^{ \frac{ 4 }{ 5 } -1 }$$

Differentiate w.r.t. x

$$-\frac{3}{80x^{\frac{6}{5}}}$$

Steps Using Definition of a Derivative

Subtract 1 from \frac{4}{5} to get -\frac{1}{5}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3}{16}x^{-\frac{1}{5}})$$

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

$$-\frac{1}{5}\times \frac{3}{16}x^{-\frac{1}{5}-1}$$

Multiply -\frac{1}{5} times \frac{3}{16} by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

$$-\frac{3}{80}x^{-\frac{1}{5}-1}$$

Subtract 1 from -\frac{1}{5}.

$$-\frac{3}{80}x^{-\frac{6}{5}}$$

Evaluate

$$\frac{3}{16\sqrt[5]{x}}$$

Solution Steps

Subtract 1 from \frac{4}{5} to get -\frac{1}{5}.

$$\frac{3}{16}x^{-\frac{1}{5}}$$