Solve -x^3div-40x^14*-15x^6

$$- { x }^{ 3 } \div -40 { x }^{ 14 } \times -15 { x }^{ 6 }$$

Evaluate

$$-\frac{3x^{23}}{8}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 14 and 6 to get 20.

$$\frac{-x^{3}}{-40}x^{20}\left(-15\right)$$

Express \frac{-x^{3}}{-40}x^{20} as a single fraction.

$$\frac{\left(-x^{3}\right)x^{20}}{-40}\left(-15\right)$$

Express \frac{\left(-x^{3}\right)x^{20}}{-40}\left(-15\right) as a single fraction.

$$\frac{-\left(-x^{3}\right)x^{20}\times 15}{-40}$$

Multiply -1 and 15 to get -15.

$$\frac{-15\left(-x^{3}\right)x^{20}}{-40}$$

Multiply -15 and -1 to get 15.

$$\frac{15x^{3}x^{20}}{-40}$$

To multiply powers of the same base, add their exponents. Add 3 and 20 to get 23.

$$\frac{15x^{23}}{-40}$$

Divide 15x^{23} by -40 to get -\frac{3}{8}x^{23}.

$$-\frac{3}{8}x^{23}$$

Differentiate w.r.t. x

$$-\frac{69x^{22}}{8}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 14 and 6 to get 20.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-x^{3}}{-40}x^{20}\left(-15\right))$$

Express \frac{-x^{3}}{-40}x^{20} as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\left(-x^{3}\right)x^{20}}{-40}\left(-15\right))$$

Express \frac{\left(-x^{3}\right)x^{20}}{-40}\left(-15\right) as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-\left(-x^{3}\right)x^{20}\times 15}{-40})$$

Multiply -1 and 15 to get -15.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-15\left(-x^{3}\right)x^{20}}{-40})$$

Multiply -15 and -1 to get 15.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{15x^{3}x^{20}}{-40})$$

To multiply powers of the same base, add their exponents. Add 3 and 20 to get 23.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{15x^{23}}{-40})$$

Divide 15x^{23} by -40 to get -\frac{3}{8}x^{23}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-\frac{3}{8}x^{23})$$

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

$$23\left(-\frac{3}{8}\right)x^{23-1}$$

Multiply 23 times -\frac{3}{8}.

$$-\frac{69}{8}x^{23-1}$$

Subtract 1 from 23.

$$-\frac{69}{8}x^{22}$$