Solve 2/3x:1/6x^3

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

Evaluate

$$4x^{4}$$

Solution Steps

Divide \frac{2}{3}x by \frac{1}{6} by multiplying \frac{2}{3}x by the reciprocal of \frac{1}{6}.

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

Multiply \frac{2}{3} and 6 to get 4.

$$4xx^{3}$$

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$4x^{4}$$

Differentiate w.r.t. x

$$16x^{3}$$

Steps Using Definition of a Derivative

Divide \frac{2}{3}x by \frac{1}{6} by multiplying \frac{2}{3}x by the reciprocal of \frac{1}{6}.

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

Multiply \frac{2}{3} and 6 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4xx^{3})$$

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x^{4})$$

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

$$4\times 4x^{4-1}$$

Multiply 4 times 4.

$$16x^{4-1}$$

Subtract 1 from 4.

$$16x^{3}$$