Solve -3x^4*4x^3

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

Evaluate

$$-12x^{7}$$

Solution Steps

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

$$-3x^{7}\times 4$$

Multiply -3 and 4 to get -12.

$$-12x^{7}$$

Differentiate w.r.t. x

$$-84x^{6}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(-3x^{7}\times 4)$$

Multiply -3 and 4 to get -12.

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

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

$$7\left(-12\right)x^{7-1}$$

Multiply 7 times -12.

$$-84x^{7-1}$$

Subtract 1 from 7.

$$-84x^{6}$$