Solve -(x)^6div(-x)^4div(-x)

$$- ( x ) ^ { 6 } \div ( - x ) ^ { 4 } \div ( - x )$$

Evaluate

$$x$$

Solution Steps

Express \frac{\frac{-x^{6}}{\left(-x\right)^{4}}}{-x} as a single fraction.

$$\frac{-x^{6}}{\left(-x\right)^{4}\left(-x\right)}$$

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

$$\frac{-x^{6}}{\left(-x\right)^{5}}$$

Expand \left(-x\right)^{5}.

$$\frac{-x^{6}}{\left(-1\right)^{5}x^{5}}$$

Calculate -1 to the power of 5 and get -1.

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

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

$$x$$

Differentiate w.r.t. x

$$1$$

Steps Using Definition of a Derivative

Express \frac{\frac{-x^{6}}{\left(-x\right)^{4}}}{-x} as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-x^{6}}{\left(-x\right)^{4}\left(-x\right)})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-x^{6}}{\left(-x\right)^{5}})$$

Expand \left(-x\right)^{5}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-x^{6}}{\left(-1\right)^{5}x^{5}})$$

Calculate -1 to the power of 5 and get -1.

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

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

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

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

$$x^{1-1}$$

Subtract 1 from 1.

$$x^{0}$$

For any term t except 0, t^{0}=1.

$$1$$