Solve (-2/5x)(-15/8x)

$$( - \frac { 2 } { 5 } x ) ( - \frac { 15 } { 8 } x )$$

Evaluate

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

Solution Steps

Multiply x and x to get x^{2}.

$$-\frac{2}{5}x^{2}\left(-\frac{15}{8}\right)$$

Multiply -\frac{2}{5} times -\frac{15}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-2\left(-15\right)}{5\times 8}x^{2}$$

Do the multiplications in the fraction \frac{-2\left(-15\right)}{5\times 8}.

$$\frac{30}{40}x^{2}$$

Reduce the fraction \frac{30}{40} to lowest terms by extracting and canceling out 10.

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

Differentiate w.r.t. x

$$\frac{3x}{2}$$

Steps Using Definition of a Derivative

Multiply x and x to get x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-\frac{2}{5}x^{2}\left(-\frac{15}{8}\right))$$

Multiply -\frac{2}{5} times -\frac{15}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-2\left(-15\right)}{5\times 8}x^{2})$$

Do the multiplications in the fraction \frac{-2\left(-15\right)}{5\times 8}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{30}{40}x^{2})$$

Reduce the fraction \frac{30}{40} to lowest terms by extracting and canceling out 10.

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

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

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

Multiply 2 times \frac{3}{4}.

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

Subtract 1 from 2.

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

For any term t, t^{1}=t.

$$\frac{3}{2}x$$