Solve 3x^2(-7x^6)

$$3 { x }^{ 2 } (-7 { x }^{ 6 } )$$

Evaluate

$$-21x^{8}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 6 to get 8.

$$3x^{8}\left(-7\right)$$

Multiply 3 and -7 to get -21.

$$-21x^{8}$$

Differentiate w.r.t. x

$$-168x^{7}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 2 and 6 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3x^{8}\left(-7\right))$$

Multiply 3 and -7 to get -21.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-21x^{8})$$

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

$$8\left(-21\right)x^{8-1}$$

Multiply 8 times -21.

$$-168x^{8-1}$$

Subtract 1 from 8.

$$-168x^{7}$$