Solve 3*1/4x^4*2/3

$$3 \times \frac { 1 } { 4 } x ^ { 4 } \times \frac { 2 } { 3 }$$

Evaluate

$$\frac{x^{4}}{2}$$

Solution Steps

Multiply 3 and \frac{1}{4} to get \frac{3}{4}.

$$\frac{3}{4}x^{4}\times \frac{2}{3}$$

Multiply \frac{3}{4} and \frac{2}{3} to get \frac{1}{2}.

$$\frac{1}{2}x^{4}$$

Differentiate w.r.t. x

$$2x^{3}$$

Steps Using Definition of a Derivative

Multiply 3 and \frac{1}{4} to get \frac{3}{4}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3}{4}x^{4}\times \frac{2}{3})$$

Multiply \frac{3}{4} and \frac{2}{3} to get \frac{1}{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{2}x^{4})$$

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

$$4\times \frac{1}{2}x^{4-1}$$

Multiply 4 times \frac{1}{2}.

$$2x^{4-1}$$

Subtract 1 from 4.

$$2x^{3}$$