Solve 7x*(-8x^2)=

$$7 x \cdot ( - 8 x ^ { 2 } ) =$$

Evaluate

$$-56x^{3}$$

Solution Steps

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

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

Multiply 7 and -8 to get -56.

$$-56x^{3}$$

Differentiate w.r.t. x

$$-168x^{2}$$

Steps Using Definition of a Derivative

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

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

Multiply 7 and -8 to get -56.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-56x^{3})$$

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

$$3\left(-56\right)x^{3-1}$$

Multiply 3 times -56.

$$-168x^{3-1}$$

Subtract 1 from 3.

$$-168x^{2}$$