Solve 6beta^10/8

$$6 \frac { \beta ^ { 10 } } { 8 }$$

Evaluate

$$\frac{3\beta ^{10}}{4}$$

Solution Steps

Express 6\times \frac{\beta ^{10}}{8} as a single fraction.

$$\frac{6\beta ^{10}}{8}$$

Divide 6\beta ^{10} by 8 to get \frac{3}{4}\beta ^{10}.

$$\frac{3}{4}\beta ^{10}$$

Differentiate w.r.t. β

$$\frac{15\beta ^{9}}{2}$$

Steps Using Definition of a Derivative

Express 6\times \frac{\beta ^{10}}{8} as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}\beta }(\frac{6\beta ^{10}}{8})$$

Divide 6\beta ^{10} by 8 to get \frac{3}{4}\beta ^{10}.

$$\frac{\mathrm{d}}{\mathrm{d}\beta }(\frac{3}{4}\beta ^{10})$$

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

$$10\times \frac{3}{4}\beta ^{10-1}$$

Multiply 10 times \frac{3}{4}.

$$\frac{15}{2}\beta ^{10-1}$$

Subtract 1 from 10.

$$\frac{15}{2}\beta ^{9}$$