Solve 12x^4*3x^3

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

Evaluate

$$36x^{7}$$

Solution Steps

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

$$12x^{7}\times 3$$

Multiply 12 and 3 to get 36.

$$36x^{7}$$

Differentiate w.r.t. x

$$252x^{6}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(12x^{7}\times 3)$$

Multiply 12 and 3 to get 36.

$$\frac{\mathrm{d}}{\mathrm{d}x}(36x^{7})$$

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

$$7\times 36x^{7-1}$$

Multiply 7 times 36.

$$252x^{7-1}$$

Subtract 1 from 7.

$$252x^{6}$$