Solve 3x^4*4x^4

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

Evaluate

$$12x^{8}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and 4 to get 8.

$$3x^{8}\times 4$$

Multiply 3 and 4 to get 12.

$$12x^{8}$$

Differentiate w.r.t. x

$$96x^{7}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 4 and 4 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3x^{8}\times 4)$$

Multiply 3 and 4 to get 12.

$$\frac{\mathrm{d}}{\mathrm{d}x}(12x^{8})$$

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

$$8\times 12x^{8-1}$$

Multiply 8 times 12.

$$96x^{8-1}$$

Subtract 1 from 8.

$$96x^{7}$$