Solve +4/9a^2*(+6/5a^-1)=

$$+ \frac { 4 } { 9 } a ^ { 2 } \cdot ( + \frac { 6 } { 5 } a ^ { - 1 } ) =$$

Evaluate

$$\frac{8a}{15}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and -1 to get 1.

$$\frac{4}{9}a^{1}\times \frac{6}{5}$$

Calculate a to the power of 1 and get a.

$$\frac{4}{9}a\times \frac{6}{5}$$

Multiply \frac{4}{9} and \frac{6}{5} to get \frac{8}{15}.

$$\frac{8}{15}a$$

Differentiate w.r.t. a

$$\frac{8}{15} = 0.5333333333333333$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 2 and -1 to get 1.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{4}{9}a^{1}\times \frac{6}{5})$$

Calculate a to the power of 1 and get a.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{4}{9}a\times \frac{6}{5})$$

Multiply \frac{4}{9} and \frac{6}{5} to get \frac{8}{15}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{8}{15}a)$$

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

$$\frac{8}{15}a^{1-1}$$

Subtract 1 from 1.

$$\frac{8}{15}a^{0}$$

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

$$\frac{8}{15}\times 1$$

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

$$\frac{8}{15}$$