Solve x(2x^2/1,2)

$$x ( \frac { 2 x ^ { 2 } } { 1,2 } )$$

Evaluate

$$\frac{5x^{3}}{3}$$

Solution Steps

Divide 2x^{2} by 1,2 to get \frac{5}{3}x^{2}.

$$x\times \frac{5}{3}x^{2}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$x^{3}\times \frac{5}{3}$$

Differentiate w.r.t. x

$$5x^{2}$$

Steps Using Definition of a Derivative

Divide 2x^{2} by 1,2 to get \frac{5}{3}x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x\times \frac{5}{3}x^{2})$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{3}\times \frac{5}{3})$$

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

$$3\times \frac{5}{3}x^{3-1}$$

Multiply 3 times \frac{5}{3}.

$$5x^{3-1}$$

Subtract 1 from 3.

$$5x^{2}$$