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

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

Evaluate

$$-\frac{12x^{8}}{5}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 7 and 1 to get 8.

$$-3x^{8}\times \frac{4}{5}$$

Multiply -3 and \frac{4}{5} to get -\frac{12}{5}.

$$-\frac{12}{5}x^{8}$$

Differentiate w.r.t. x

$$-\frac{96x^{7}}{5}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 7 and 1 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-3x^{8}\times \frac{4}{5})$$

Multiply -3 and \frac{4}{5} to get -\frac{12}{5}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-\frac{12}{5}x^{8})$$

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

$$8\left(-\frac{12}{5}\right)x^{8-1}$$

Multiply 8 times -\frac{12}{5}.

$$-\frac{96}{5}x^{8-1}$$

Subtract 1 from 8.

$$-\frac{96}{5}x^{7}$$