Solve Delta(-3/4)^2*8/27/2

$$\frac { \Delta ( - \frac { 3 } { 4 } ) ^ { 2 } \times \frac { 8 } { 27 } } { 2 }$$

Evaluate

$$\frac{\Delta }{12}$$

Solution Steps

Calculate -\frac{3}{4} to the power of 2 and get \frac{9}{16}.

$$\frac{\Delta \times \frac{9}{16}\times \frac{8}{27}}{2}$$

Multiply \frac{9}{16} times \frac{8}{27} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\Delta \times \frac{9\times 8}{16\times 27}}{2}$$

Do the multiplications in the fraction \frac{9\times 8}{16\times 27}.

$$\frac{\Delta \times \frac{72}{432}}{2}$$

Reduce the fraction \frac{72}{432} to lowest terms by extracting and canceling out 72.

$$\frac{\Delta \times \frac{1}{6}}{2}$$

Divide \Delta \times \frac{1}{6} by 2 to get \Delta \times \frac{1}{12}.

$$\Delta \times \frac{1}{12}$$

Differentiate w.r.t. Δ

$$\frac{1}{12} = 0.08333333333333333$$

Steps Using Definition of a Derivative

Calculate -\frac{3}{4} to the power of 2 and get \frac{9}{16}.

$$\frac{\mathrm{d}}{\mathrm{d}\Delta }(\frac{\Delta \times \frac{9}{16}\times \frac{8}{27}}{2})$$

Multiply \frac{9}{16} times \frac{8}{27} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}\Delta }(\frac{\Delta \times \frac{9\times 8}{16\times 27}}{2})$$

Do the multiplications in the fraction \frac{9\times 8}{16\times 27}.

$$\frac{\mathrm{d}}{\mathrm{d}\Delta }(\frac{\Delta \times \frac{72}{432}}{2})$$

Reduce the fraction \frac{72}{432} to lowest terms by extracting and canceling out 72.

$$\frac{\mathrm{d}}{\mathrm{d}\Delta }(\frac{\Delta \times \frac{1}{6}}{2})$$

Divide \Delta \times \frac{1}{6} by 2 to get \Delta \times \frac{1}{12}.

$$\frac{\mathrm{d}}{\mathrm{d}\Delta }(\Delta \times \frac{1}{12})$$

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

$$\frac{1}{12}\Delta ^{1-1}$$

Subtract 1 from 1.

$$\frac{1}{12}\Delta ^{0}$$

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

$$\frac{1}{12}\times 1$$

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

$$\frac{1}{12}$$