Solve -6x^7div52x^8div5

$$-6 { x }^{ 7 \div 5 } 2 { x }^{ 8 \div 5 }$$

Evaluate

$$-12x^{3}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add \frac{7}{5} and \frac{8}{5} to get 3.

$$-6x^{3}\times 2$$

Multiply -6 and 2 to get -12.

$$-12x^{3}$$

Differentiate w.r.t. x

$$-36x^{2}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add \frac{7}{5} and \frac{8}{5} to get 3.

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

Multiply -6 and 2 to get -12.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-12x^{3})$$

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

$$3\left(-12\right)x^{3-1}$$

Multiply 3 times -12.

$$-36x^{3-1}$$

Subtract 1 from 3.

$$-36x^{2}$$