Solve 3^8/15g-5^1/2g-1^1/10g-2^5/6g

$$3 ^ { 8 } / 15 g - 5 ^ { 1 } / 2 g - 1 ^ { 1 } / 10 g - 2 ^ { 5 } / 6 g$$

Evaluate

$$\frac{6442g}{15}$$

Solution Steps

Calculate 3 to the power of 8 and get 6561.

$$\frac{6561}{15}g-\frac{5^{1}}{2}g-\frac{1^{1}}{10}g-\frac{2^{5}}{6}g$$

Reduce the fraction \frac{6561}{15} to lowest terms by extracting and canceling out 3.

$$\frac{2187}{5}g-\frac{5^{1}}{2}g-\frac{1^{1}}{10}g-\frac{2^{5}}{6}g$$

Calculate 5 to the power of 1 and get 5.

$$\frac{2187}{5}g-\frac{5}{2}g-\frac{1^{1}}{10}g-\frac{2^{5}}{6}g$$

Combine \frac{2187}{5}g and -\frac{5}{2}g to get \frac{4349}{10}g.

$$\frac{4349}{10}g-\frac{1^{1}}{10}g-\frac{2^{5}}{6}g$$

Calculate 1 to the power of 1 and get 1.

$$\frac{4349}{10}g-\frac{1}{10}g-\frac{2^{5}}{6}g$$

Combine \frac{4349}{10}g and -\frac{1}{10}g to get \frac{2174}{5}g.

$$\frac{2174}{5}g-\frac{2^{5}}{6}g$$

Calculate 2 to the power of 5 and get 32.

$$\frac{2174}{5}g-\frac{32}{6}g$$

Reduce the fraction \frac{32}{6} to lowest terms by extracting and canceling out 2.

$$\frac{2174}{5}g-\frac{16}{3}g$$

Combine \frac{2174}{5}g and -\frac{16}{3}g to get \frac{6442}{15}g.

$$\frac{6442}{15}g$$

Differentiate w.r.t. g

$$\frac{6442}{15} = 429\frac{7}{15} = 429.46666666666664$$

Steps Using Definition of a Derivative

Calculate 3 to the power of 8 and get 6561.

$$\frac{\mathrm{d}}{\mathrm{d}g}(\frac{6561}{15}g-\frac{5^{1}}{2}g-\frac{1^{1}}{10}g-\frac{2^{5}}{6}g)$$

Reduce the fraction \frac{6561}{15} to lowest terms by extracting and canceling out 3.

$$\frac{\mathrm{d}}{\mathrm{d}g}(\frac{2187}{5}g-\frac{5^{1}}{2}g-\frac{1^{1}}{10}g-\frac{2^{5}}{6}g)$$

Calculate 5 to the power of 1 and get 5.

$$\frac{\mathrm{d}}{\mathrm{d}g}(\frac{2187}{5}g-\frac{5}{2}g-\frac{1^{1}}{10}g-\frac{2^{5}}{6}g)$$

Combine \frac{2187}{5}g and -\frac{5}{2}g to get \frac{4349}{10}g.

$$\frac{\mathrm{d}}{\mathrm{d}g}(\frac{4349}{10}g-\frac{1^{1}}{10}g-\frac{2^{5}}{6}g)$$

Calculate 1 to the power of 1 and get 1.

$$\frac{\mathrm{d}}{\mathrm{d}g}(\frac{4349}{10}g-\frac{1}{10}g-\frac{2^{5}}{6}g)$$

Combine \frac{4349}{10}g and -\frac{1}{10}g to get \frac{2174}{5}g.

$$\frac{\mathrm{d}}{\mathrm{d}g}(\frac{2174}{5}g-\frac{2^{5}}{6}g)$$

Calculate 2 to the power of 5 and get 32.

$$\frac{\mathrm{d}}{\mathrm{d}g}(\frac{2174}{5}g-\frac{32}{6}g)$$

Reduce the fraction \frac{32}{6} to lowest terms by extracting and canceling out 2.

$$\frac{\mathrm{d}}{\mathrm{d}g}(\frac{2174}{5}g-\frac{16}{3}g)$$

Combine \frac{2174}{5}g and -\frac{16}{3}g to get \frac{6442}{15}g.

$$\frac{\mathrm{d}}{\mathrm{d}g}(\frac{6442}{15}g)$$

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

$$\frac{6442}{15}g^{1-1}$$

Subtract 1 from 1.

$$\frac{6442}{15}g^{0}$$

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

$$\frac{6442}{15}\times 1$$

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

$$\frac{6442}{15}$$