Solve g*(sqrt[5]{frac{243/32})^3}{sqrt{5^0}}

$$g \cdot \frac { ( \sqrt[ 5 ] { \frac { 243 } { 32 } } ) ^ { 3 } } { \sqrt { 5 ^ { 0 } } }$$

Evaluate

$$\frac{27g}{8}$$

Solution Steps

Calculate \sqrt[5]{\frac{243}{32}} and get \frac{3}{2}.

$$g\times \frac{\left(\frac{3}{2}\right)^{3}}{\sqrt{5^{0}}}$$

Calculate \frac{3}{2} to the power of 3 and get \frac{27}{8}.

$$g\times \frac{\frac{27}{8}}{\sqrt{5^{0}}}$$

Calculate 5 to the power of 0 and get 1.

$$g\times \frac{\frac{27}{8}}{\sqrt{1}}$$

Calculate the square root of 1 and get 1.

$$g\times \frac{\frac{27}{8}}{1}$$

Anything divided by one gives itself.

$$g\times \frac{27}{8}$$

Differentiate w.r.t. g

$$\frac{27}{8} = 3\frac{3}{8} = 3.375$$

Steps Using Definition of a Derivative

Calculate \sqrt[5]{\frac{243}{32}} and get \frac{3}{2}.

$$\frac{\mathrm{d}}{\mathrm{d}g}(g\times \frac{\left(\frac{3}{2}\right)^{3}}{\sqrt{5^{0}}})$$

Calculate \frac{3}{2} to the power of 3 and get \frac{27}{8}.

$$\frac{\mathrm{d}}{\mathrm{d}g}(g\times \frac{\frac{27}{8}}{\sqrt{5^{0}}})$$

Calculate 5 to the power of 0 and get 1.

$$\frac{\mathrm{d}}{\mathrm{d}g}(g\times \frac{\frac{27}{8}}{\sqrt{1}})$$

Calculate the square root of 1 and get 1.

$$\frac{\mathrm{d}}{\mathrm{d}g}(g\times \frac{\frac{27}{8}}{1})$$

Anything divided by one gives itself.

$$\frac{\mathrm{d}}{\mathrm{d}g}(g\times \frac{27}{8})$$

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

$$\frac{27}{8}g^{1-1}$$

Subtract 1 from 1.

$$\frac{27}{8}g^{0}$$

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

$$\frac{27}{8}\times 1$$

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

$$\frac{27}{8}$$