Solve frac{x^{2}*x^4*x^5}{x^5*x^2}

$$\frac { x ^ { 2 } \cdot x ^ { 4 } \cdot x ^ { 5 } } { x ^ { 5 } \cdot x ^ { 2 } }$$

Evaluate

$$x^{4}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 4 to get 6.

$$\frac{x^{6}x^{5}}{x^{5}x^{2}}$$

To multiply powers of the same base, add their exponents. Add 6 and 5 to get 11.

$$\frac{x^{11}}{x^{5}x^{2}}$$

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

$$\frac{x^{11}}{x^{7}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 7 from 11 to get 4.

$$x^{4}$$

Differentiate w.r.t. x

$$4x^{3}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 2 and 4 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{6}x^{5}}{x^{5}x^{2}})$$

To multiply powers of the same base, add their exponents. Add 6 and 5 to get 11.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{11}}{x^{5}x^{2}})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{11}}{x^{7}})$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 7 from 11 to get 4.

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

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

$$4x^{4-1}$$

Subtract 1 from 4.

$$4x^{3}$$