Solve (5x^2)(2x^2)(-3x^2)

$$( 5 x ^ { 2 } ) ( 2 x ^ { 2 } ) ( - 3 x ^ { 2 } )$$

Evaluate

$$-30x^{6}$$

Solution Steps

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

$$5x^{4}\times 2\left(-3\right)x^{2}$$

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

$$5x^{6}\times 2\left(-3\right)$$

Multiply 5 and 2 to get 10.

$$10x^{6}\left(-3\right)$$

Multiply 10 and -3 to get -30.

$$-30x^{6}$$

Differentiate w.r.t. x

$$-180x^{5}$$

Steps Using Definition of a Derivative

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

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

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}x}(5x^{6}\times 2\left(-3\right))$$

Multiply 5 and 2 to get 10.

$$\frac{\mathrm{d}}{\mathrm{d}x}(10x^{6}\left(-3\right))$$

Multiply 10 and -3 to get -30.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-30x^{6})$$

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

$$6\left(-30\right)x^{6-1}$$

Multiply 6 times -30.

$$-180x^{6-1}$$

Subtract 1 from 6.

$$-180x^{5}$$