Solve 12x^4*-5x^3

$$12 x ^ { 4 } \cdot - 5 x ^ { 3 }$$

Evaluate

$$-60x^{7}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and 3 to get 7.

$$12x^{7}\left(-5\right)$$

Multiply 12 and -5 to get -60.

$$-60x^{7}$$

Differentiate w.r.t. x

$$-420x^{6}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 4 and 3 to get 7.

$$\frac{\mathrm{d}}{\mathrm{d}x}(12x^{7}\left(-5\right))$$

Multiply 12 and -5 to get -60.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-60x^{7})$$

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

$$7\left(-60\right)x^{7-1}$$

Multiply 7 times -60.

$$-420x^{7-1}$$

Subtract 1 from 7.

$$-420x^{6}$$