Solve 15/7*11/8x3/13

$$\frac { 15 } { 7 } * \frac { 11 } { 8 } x \frac { 3 } { 13 }$$

Evaluate

$$\frac{495x}{728}$$

Solution Steps

Multiply \frac{15}{7} times \frac{11}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{15\times 11}{7\times 8}x\times \frac{3}{13}$$

Do the multiplications in the fraction \frac{15\times 11}{7\times 8}.

$$\frac{165}{56}x\times \frac{3}{13}$$

Multiply \frac{165}{56} times \frac{3}{13} by multiplying numerator times numerator and denominator times denominator.

$$\frac{165\times 3}{56\times 13}x$$

Do the multiplications in the fraction \frac{165\times 3}{56\times 13}.

$$\frac{495}{728}x$$

Differentiate w.r.t. x

$$\frac{495}{728} = 0.679945054945055$$

Steps Using Definition of a Derivative

Multiply \frac{15}{7} times \frac{11}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{15\times 11}{7\times 8}x\times \frac{3}{13})$$

Do the multiplications in the fraction \frac{15\times 11}{7\times 8}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{165}{56}x\times \frac{3}{13})$$

Multiply \frac{165}{56} times \frac{3}{13} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{165\times 3}{56\times 13}x)$$

Do the multiplications in the fraction \frac{165\times 3}{56\times 13}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{495}{728}x)$$

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

$$\frac{495}{728}x^{1-1}$$

Subtract 1 from 1.

$$\frac{495}{728}x^{0}$$

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

$$\frac{495}{728}\times 1$$

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

$$\frac{495}{728}$$