Solve x^3*x^5+x*x^7

$$x ^ { 3 } \cdot x ^ { 5 } + x \cdot x ^ { 7 }$$

Evaluate

$$2x^{8}$$

Solution Steps

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

$$x^{8}+xx^{7}$$

To multiply powers of the same base, add their exponents. Add 1 and 7 to get 8.

$$x^{8}+x^{8}$$

Combine x^{8} and x^{8} to get 2x^{8}.

$$2x^{8}$$

Differentiate w.r.t. x

$$16x^{7}$$

Steps Using Definition of a Derivative

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

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

To multiply powers of the same base, add their exponents. Add 1 and 7 to get 8.

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

Combine x^{8} and x^{8} to get 2x^{8}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{8})$$

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

$$8\times 2x^{8-1}$$

Multiply 8 times 2.

$$16x^{8-1}$$

Subtract 1 from 8.

$$16x^{7}$$