Solve 4/5x^3(-7/2x^2)

$$\frac { 4 } { 5 } x ^ { 3 } ( - \frac { 7 } { 2 } x ^ { 2 } )$$

Evaluate

$$-\frac{14x^{5}}{5}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$\frac{4}{5}x^{5}\left(-\frac{7}{2}\right)$$

Multiply \frac{4}{5} and -\frac{7}{2} to get -\frac{14}{5}.

$$-\frac{14}{5}x^{5}$$

Differentiate w.r.t. x

$$-14x^{4}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{4}{5}x^{5}\left(-\frac{7}{2}\right))$$

Multiply \frac{4}{5} and -\frac{7}{2} to get -\frac{14}{5}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-\frac{14}{5}x^{5})$$

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

$$5\left(-\frac{14}{5}\right)x^{5-1}$$

Multiply 5 times -\frac{14}{5}.

$$-14x^{5-1}$$

Subtract 1 from 5.

$$-14x^{4}$$