Solve x^2x^3+xx^4

$$x ^ { 2 } x ^ { 3 } + x x ^ { 4 }$$

Evaluate

$$2x^{5}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$x^{5}+xx^{4}$$

To multiply powers of the same base, add their exponents. Add 1 and 4 to get 5.

$$x^{5}+x^{5}$$

Combine x^{5} and x^{5} to get 2x^{5}.

$$2x^{5}$$

Differentiate w.r.t. x

$$10x^{4}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{5}+xx^{4})$$

To multiply powers of the same base, add their exponents. Add 1 and 4 to get 5.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{5}+x^{5})$$

Combine x^{5} and x^{5} to get 2x^{5}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{5})$$

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

$$5\times 2x^{5-1}$$

Multiply 5 times 2.

$$10x^{5-1}$$

Subtract 1 from 5.

$$10x^{4}$$