Solve x^2*x^3*x^5

$$x ^ { 2 } \cdot x ^ { 3 } \cdot x ^ { 5 }$$

Evaluate

$$x^{10}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$x^{2}x^{3}x^{5}$$

Use the Multiplication Rule for Exponents.

$$x^{2+3+5}$$

Add the exponents 2 and 3.

$$x^{5+5}$$

Add the exponents 5 and 5.

$$x^{10}$$

Differentiate w.r.t. x

$$10x^{9}$$

Steps Using Definition of a Derivative

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

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

To multiply powers of the same base, add their exponents. Add 5 and 5 to get 10.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{10})$$

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

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

Subtract 1 from 10.

$$10x^{9}$$