Solve 3x^2*(-7x)

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

Evaluate

$$-21x^{3}$$

Solution Steps

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

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

Multiply 3 and -7 to get -21.

$$-21x^{3}$$

Differentiate w.r.t. x

$$-63x^{2}$$

Steps Using Definition of a Derivative

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

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

Multiply 3 and -7 to get -21.

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

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

$$3\left(-21\right)x^{3-1}$$

Multiply 3 times -21.

$$-63x^{3-1}$$

Subtract 1 from 3.

$$-63x^{2}$$