Solve (-x^2)*(-8/5x^2)

$$(- { x }^{ 2 } ) \times (- \frac{ 8 }{ 5 } { x }^{ 2 } )$$

Evaluate

$$\frac{8x^{4}}{5}$$

Solution Steps

Multiply -1 and -\frac{8}{5} to get \frac{8}{5}.

$$\frac{8}{5}x^{2}x^{2}$$

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$\frac{8}{5}x^{4}$$

Differentiate w.r.t. x

$$\frac{32x^{3}}{5}$$

Steps Using Definition of a Derivative

Multiply -1 and -\frac{8}{5} to get \frac{8}{5}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{8}{5}x^{2}x^{2})$$

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

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

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

$$4\times \frac{8}{5}x^{4-1}$$

Multiply 4 times \frac{8}{5}.

$$\frac{32}{5}x^{4-1}$$

Subtract 1 from 4.

$$\frac{32}{5}x^{3}$$