Solve 12x^-frac{1{5}}div3x

$$12 x ^ { - \frac { 1 } { 5 } } \div 3 x$$

Evaluate

$$4x^{\frac{4}{5}}$$

Solution Steps

Divide 12x^{-\frac{1}{5}} by 3 to get 4x^{-\frac{1}{5}}.

$$4x^{-\frac{1}{5}}x$$

To multiply powers of the same base, add their exponents. Add -\frac{1}{5} and 1 to get \frac{4}{5}.

$$4x^{\frac{4}{5}}$$

Differentiate w.r.t. x

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

Steps Using Definition of a Derivative

Divide 12x^{-\frac{1}{5}} by 3 to get 4x^{-\frac{1}{5}}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x^{-\frac{1}{5}}x)$$

To multiply powers of the same base, add their exponents. Add -\frac{1}{5} and 1 to get \frac{4}{5}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x^{\frac{4}{5}})$$

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

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

Multiply \frac{4}{5} times 4.

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

Subtract 1 from \frac{4}{5}.

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