Solve x^5x^2x/x^3x^2

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

Evaluate

$$x^{3}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 5 and 2 to get 7.

$$\frac{x^{7}x}{x^{3}x^{2}}$$

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

$$\frac{x^{8}}{x^{3}x^{2}}$$

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

$$\frac{x^{8}}{x^{5}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 5 from 8 to get 3.

$$x^{3}$$

Differentiate w.r.t. x

$$3x^{2}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 5 and 2 to get 7.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{7}x}{x^{3}x^{2}})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{8}}{x^{3}x^{2}})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{8}}{x^{5}})$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 5 from 8 to get 3.

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

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

$$3x^{3-1}$$

Subtract 1 from 3.

$$3x^{2}$$