Solve 3x^4*4x^3

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

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}.

$$7\times 12x^{7-1}$$

Multiply 7 times 12.

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

Subtract 1 from 7.

$$84x^{6}$$