Solve (7x^2)(3x)(-x^2)

$$( 7 x ^ { 2 } ) ( 3 x ) ( - x ^ { 2 } )$$

Evaluate

$$-21x^{5}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$7x^{3}\times 3\left(-x^{2}\right)$$

Multiply 7 and 3 to get 21.

$$21x^{3}\left(-x^{2}\right)$$

Multiply 21 and -1 to get -21.

$$-21x^{3}x^{2}$$

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

$$-21x^{5}$$

Differentiate w.r.t. x

$$-105x^{4}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\frac{\mathrm{d}}{\mathrm{d}x}(7x^{3}\times 3\left(-x^{2}\right))$$

Multiply 7 and 3 to get 21.

$$\frac{\mathrm{d}}{\mathrm{d}x}(21x^{3}\left(-x^{2}\right))$$

Multiply 21 and -1 to get -21.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-21x^{3}x^{2})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(-21x^{5})$$

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

$$5\left(-21\right)x^{5-1}$$

Multiply 5 times -21.

$$-105x^{5-1}$$

Subtract 1 from 5.

$$-105x^{4}$$