Solve 52/5*1.5*3v

$$52 / 5 \cdot 1.5 \times 3 v$$

Evaluate

$$\frac{234v}{5}$$

Solution Steps

Convert decimal number 1.5 to fraction \frac{15}{10}. Reduce the fraction \frac{15}{10} to lowest terms by extracting and canceling out 5.

$$\frac{52}{5}\times \frac{3}{2}\times 3v$$

Multiply \frac{52}{5} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{52\times 3}{5\times 2}\times 3v$$

Do the multiplications in the fraction \frac{52\times 3}{5\times 2}.

$$\frac{156}{10}\times 3v$$

Reduce the fraction \frac{156}{10} to lowest terms by extracting and canceling out 2.

$$\frac{78}{5}\times 3v$$

Express \frac{78}{5}\times 3 as a single fraction.

$$\frac{78\times 3}{5}v$$

Multiply 78 and 3 to get 234.

$$\frac{234}{5}v$$

Differentiate w.r.t. v

$$46.8$$

Steps Using Definition of a Derivative

Convert decimal number 1.5 to fraction \frac{15}{10}. Reduce the fraction \frac{15}{10} to lowest terms by extracting and canceling out 5.

$$\frac{\mathrm{d}}{\mathrm{d}v}(\frac{52}{5}\times \frac{3}{2}\times 3v)$$

Multiply \frac{52}{5} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}v}(\frac{52\times 3}{5\times 2}\times 3v)$$

Do the multiplications in the fraction \frac{52\times 3}{5\times 2}.

$$\frac{\mathrm{d}}{\mathrm{d}v}(\frac{156}{10}\times 3v)$$

Reduce the fraction \frac{156}{10} to lowest terms by extracting and canceling out 2.

$$\frac{\mathrm{d}}{\mathrm{d}v}(\frac{78}{5}\times 3v)$$

Express \frac{78}{5}\times 3 as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}v}(\frac{78\times 3}{5}v)$$

Multiply 78 and 3 to get 234.

$$\frac{\mathrm{d}}{\mathrm{d}v}(\frac{234}{5}v)$$

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

$$\frac{234}{5}v^{1-1}$$

Subtract 1 from 1.

$$\frac{234}{5}v^{0}$$

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

$$\frac{234}{5}\times 1$$

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

$$\frac{234}{5}$$