Solve -x^12divx^4div(-x)5

$$- { x }^{ 12 } \div { x }^{ 4 } \div (-x)5$$

Evaluate

$$5x^{7}$$

Solution Steps

Express \frac{\frac{-x^{12}}{x^{4}}}{-x} as a single fraction.

$$\frac{-x^{12}}{x^{4}\left(-x\right)}\times 5$$

Express \frac{-x^{12}}{x^{4}\left(-x\right)}\times 5 as a single fraction.

$$\frac{\left(-x^{12}\right)\times 5}{x^{4}\left(-x\right)}$$

Multiply -1 and 5 to get -5.

$$\frac{-5x^{12}}{x^{4}\left(-1\right)x}$$

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

$$\frac{-5x^{12}}{x^{5}\left(-1\right)}$$

Cancel out x^{5} in both numerator and denominator.

$$\frac{-5x^{7}}{-1}$$

Anything divided by -1 gives its opposite.

$$5x^{7}$$

Differentiate w.r.t. x

$$35x^{6}$$

Steps Using Definition of a Derivative

Express \frac{\frac{-x^{12}}{x^{4}}}{-x} as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-x^{12}}{x^{4}\left(-x\right)}\times 5)$$

Express \frac{-x^{12}}{x^{4}\left(-x\right)}\times 5 as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\left(-x^{12}\right)\times 5}{x^{4}\left(-x\right)})$$

Multiply -1 and 5 to get -5.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-5x^{12}}{x^{4}\left(-1\right)x})$$

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-5x^{12}}{x^{5}\left(-1\right)})$$

Cancel out x^{5} in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-5x^{7}}{-1})$$

Anything divided by -1 gives its opposite.

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

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

$$7\times 5x^{7-1}$$

Multiply 7 times 5.

$$35x^{7-1}$$

Subtract 1 from 7.

$$35x^{6}$$