Solve -5/18x^4div2/3x

$$- \frac{ 5 }{ 18 } { x }^{ 4 } \div \frac{ 2 }{ 3 } x$$

Evaluate

$$-\frac{5x^{5}}{12}$$

Solution Steps

Divide -\frac{5}{18}x^{4} by \frac{2}{3} by multiplying -\frac{5}{18}x^{4} by the reciprocal of \frac{2}{3}.

$$\frac{-\frac{5}{18}x^{4}\times 3}{2}x$$

Multiply -\frac{5}{18} and 3 to get -\frac{5}{6}.

$$\frac{-\frac{5}{6}x^{4}}{2}x$$

Divide -\frac{5}{6}x^{4} by 2 to get -\frac{5}{12}x^{4}.

$$-\frac{5}{12}x^{4}x$$

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

$$-\frac{5}{12}x^{5}$$

Differentiate w.r.t. x

$$-\frac{25x^{4}}{12}$$

Steps Using Definition of a Derivative

Divide -\frac{5}{18}x^{4} by \frac{2}{3} by multiplying -\frac{5}{18}x^{4} by the reciprocal of \frac{2}{3}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-\frac{5}{18}x^{4}\times 3}{2}x)$$

Multiply -\frac{5}{18} and 3 to get -\frac{5}{6}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-\frac{5}{6}x^{4}}{2}x)$$

Divide -\frac{5}{6}x^{4} by 2 to get -\frac{5}{12}x^{4}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-\frac{5}{12}x^{4}x)$$

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-\frac{5}{12}x^{5})$$

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

$$5\left(-\frac{5}{12}\right)x^{5-1}$$

Multiply 5 times -\frac{5}{12}.

$$-\frac{25}{12}x^{5-1}$$

Subtract 1 from 5.

$$-\frac{25}{12}x^{4}$$