Solve -7/8x^2x^5x^6div-5/2xx^5x

$$- \frac{ 7 }{ 8 } { x }^{ 2 } { x }^{ 5 } { x }^{ 6 } \div - \frac{ 5 }{ 2 } x { x }^{ 5 } x$$

Evaluate

$$\frac{7x^{20}}{20}$$

Solution Steps

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

$$\frac{-\frac{7}{8}x^{7}x^{6}}{-\frac{5}{2}}xx^{5}x$$

To multiply powers of the same base, add their exponents. Add 7 and 6 to get 13.

$$\frac{-\frac{7}{8}x^{13}}{-\frac{5}{2}}xx^{5}x$$

To multiply powers of the same base, add their exponents. Add 1 and 5 to get 6.

$$\frac{-\frac{7}{8}x^{13}}{-\frac{5}{2}}x^{6}x$$

To multiply powers of the same base, add their exponents. Add 6 and 1 to get 7.

$$\frac{-\frac{7}{8}x^{13}}{-\frac{5}{2}}x^{7}$$

Divide -\frac{7}{8}x^{13} by -\frac{5}{2} by multiplying -\frac{7}{8}x^{13} by the reciprocal of -\frac{5}{2}.

$$\frac{-\frac{7}{8}x^{13}\times 2}{-5}x^{7}$$

Multiply -\frac{7}{8} and 2 to get -\frac{7}{4}.

$$\frac{-\frac{7}{4}x^{13}}{-5}x^{7}$$

Divide -\frac{7}{4}x^{13} by -5 to get \frac{7}{20}x^{13}.

$$\frac{7}{20}x^{13}x^{7}$$

To multiply powers of the same base, add their exponents. Add 13 and 7 to get 20.

$$\frac{7}{20}x^{20}$$

Differentiate w.r.t. x

$$7x^{19}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-\frac{7}{8}x^{7}x^{6}}{-\frac{5}{2}}xx^{5}x)$$

To multiply powers of the same base, add their exponents. Add 7 and 6 to get 13.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-\frac{7}{8}x^{13}}{-\frac{5}{2}}xx^{5}x)$$

To multiply powers of the same base, add their exponents. Add 1 and 5 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-\frac{7}{8}x^{13}}{-\frac{5}{2}}x^{6}x)$$

To multiply powers of the same base, add their exponents. Add 6 and 1 to get 7.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-\frac{7}{8}x^{13}}{-\frac{5}{2}}x^{7})$$

Divide -\frac{7}{8}x^{13} by -\frac{5}{2} by multiplying -\frac{7}{8}x^{13} by the reciprocal of -\frac{5}{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-\frac{7}{8}x^{13}\times 2}{-5}x^{7})$$

Multiply -\frac{7}{8} and 2 to get -\frac{7}{4}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-\frac{7}{4}x^{13}}{-5}x^{7})$$

Divide -\frac{7}{4}x^{13} by -5 to get \frac{7}{20}x^{13}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{7}{20}x^{13}x^{7})$$

To multiply powers of the same base, add their exponents. Add 13 and 7 to get 20.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{7}{20}x^{20})$$

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

$$20\times \frac{7}{20}x^{20-1}$$

Multiply 20 times \frac{7}{20}.

$$7x^{20-1}$$

Subtract 1 from 20.

$$7x^{19}$$