Solve -5x^2*2x^5div10x^14

$$- 5 x ^ { 2 } \times 2 x ^ { 5 } \div 10 x ^ { 14 }$$

Evaluate

$$-x^{21}$$

Solution Steps

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

$$\frac{-5x^{7}\times 2}{10}x^{14}$$

Multiply -5 and 2 to get -10.

$$\frac{-10x^{7}}{10}x^{14}$$

Cancel out 10 and 10.

$$-x^{7}x^{14}$$

To multiply powers of the same base, add their exponents. Add 7 and 14 to get 21.

$$-x^{21}$$

Differentiate w.r.t. x

$$-21x^{20}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-5x^{7}\times 2}{10}x^{14})$$

Multiply -5 and 2 to get -10.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-10x^{7}}{10}x^{14})$$

Cancel out 10 and 10.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-x^{7}x^{14})$$

To multiply powers of the same base, add their exponents. Add 7 and 14 to get 21.

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

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

$$21\left(-1\right)x^{21-1}$$

Multiply 21 times -1.

$$-21x^{21-1}$$

Subtract 1 from 21.

$$-21x^{20}$$