Solve 4x^2div12x^6

$$4 x ^ { 2 } \div 12 x ^ { 6 }$$

Evaluate

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

Solution Steps

Divide 4x^{2} by 12 to get \frac{1}{3}x^{2}.

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

To multiply powers of the same base, add their exponents. Add 2 and 6 to get 8.

$$\frac{1}{3}x^{8}$$

Differentiate w.r.t. x

$$\frac{8x^{7}}{3}$$

Steps Using Definition of a Derivative

Divide 4x^{2} by 12 to get \frac{1}{3}x^{2}.

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

To multiply powers of the same base, add their exponents. Add 2 and 6 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{3}x^{8})$$

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

$$8\times \frac{1}{3}x^{8-1}$$

Multiply 8 times \frac{1}{3}.

$$\frac{8}{3}x^{8-1}$$

Subtract 1 from 8.

$$\frac{8}{3}x^{7}$$