Solve -4x^6div8x^3

$$-4 { x }^{ 6 } \div 8 { x }^{ 3 }$$

Evaluate

$$-\frac{x^{9}}{2}$$

Solution Steps

Divide -4x^{6} by 8 to get -\frac{1}{2}x^{6}.

$$-\frac{1}{2}x^{6}x^{3}$$

To multiply powers of the same base, add their exponents. Add 6 and 3 to get 9.

$$-\frac{1}{2}x^{9}$$

Differentiate w.r.t. x

$$-\frac{9x^{8}}{2}$$

Steps Using Definition of a Derivative

Divide -4x^{6} by 8 to get -\frac{1}{2}x^{6}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-\frac{1}{2}x^{6}x^{3})$$

To multiply powers of the same base, add their exponents. Add 6 and 3 to get 9.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-\frac{1}{2}x^{9})$$

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

$$9\left(-\frac{1}{2}\right)x^{9-1}$$

Multiply 9 times -\frac{1}{2}.

$$-\frac{9}{2}x^{9-1}$$

Subtract 1 from 9.

$$-\frac{9}{2}x^{8}$$