Solve x*0.6*3/8

$$x \times 0.6 \times \frac{ 3 }{ 8 }$$

Evaluate

$$\frac{9x}{40}$$

Solution Steps

Convert decimal number 0.6 to fraction \frac{6}{10}. Reduce the fraction \frac{6}{10} to lowest terms by extracting and canceling out 2.

$$x\times \frac{3}{5}\times \frac{3}{8}$$

Multiply \frac{3}{5} times \frac{3}{8} by multiplying numerator times numerator and denominator times denominator.

$$x\times \frac{3\times 3}{5\times 8}$$

Do the multiplications in the fraction \frac{3\times 3}{5\times 8}.

$$x\times \frac{9}{40}$$

Differentiate w.r.t. x

$$0.225$$

Steps Using Definition of a Derivative

Convert decimal number 0.6 to fraction \frac{6}{10}. Reduce the fraction \frac{6}{10} to lowest terms by extracting and canceling out 2.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x\times \frac{3}{5}\times \frac{3}{8})$$

Multiply \frac{3}{5} times \frac{3}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x\times \frac{3\times 3}{5\times 8})$$

Do the multiplications in the fraction \frac{3\times 3}{5\times 8}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x\times \frac{9}{40})$$

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

$$\frac{9}{40}x^{1-1}$$

Subtract 1 from 1.

$$\frac{9}{40}x^{0}$$

For any term t except 0, t^{0}=1.

$$\frac{9}{40}\times 1$$

For any term t, t\times 1=t and 1t=t.

$$\frac{9}{40}$$