Solve 7x^3*7x^5

$$7 { x }^{ 3 } \times 7 { x }^{ 5 }$$

Evaluate

$$49x^{8}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 5 to get 8.

$$7x^{8}\times 7$$

Multiply 7 and 7 to get 49.

$$49x^{8}$$

Differentiate w.r.t. x

$$392x^{7}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 3 and 5 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}x}(7x^{8}\times 7)$$

Multiply 7 and 7 to get 49.

$$\frac{\mathrm{d}}{\mathrm{d}x}(49x^{8})$$

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

$$8\times 49x^{8-1}$$

Multiply 8 times 49.

$$392x^{8-1}$$

Subtract 1 from 8.

$$392x^{7}$$