Solve frac{x^{15}*x^14}{x^5*x^10*x^6}

$$\frac { x ^ { 15 } \cdot x ^ { 14 } } { x ^ { 5 } \cdot x ^ { 10 } \cdot x ^ { 6 } }$$

Evaluate

$$x^{8}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 15 and 14 to get 29.

$$\frac{x^{29}}{x^{5}x^{10}x^{6}}$$

To multiply powers of the same base, add their exponents. Add 5 and 10 to get 15.

$$\frac{x^{29}}{x^{15}x^{6}}$$

To multiply powers of the same base, add their exponents. Add 15 and 6 to get 21.

$$\frac{x^{29}}{x^{21}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 21 from 29 to get 8.

$$x^{8}$$

Differentiate w.r.t. x

$$8x^{7}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 15 and 14 to get 29.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{29}}{x^{5}x^{10}x^{6}})$$

To multiply powers of the same base, add their exponents. Add 5 and 10 to get 15.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{29}}{x^{15}x^{6}})$$

To multiply powers of the same base, add their exponents. Add 15 and 6 to get 21.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{29}}{x^{21}})$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 21 from 29 to get 8.

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

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

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

Subtract 1 from 8.

$$8x^{7}$$