Solve +3^1-5*a*5

$$+ 3 ^ { 1 - 5 } \times a \cdot 5$$

Evaluate

$$\frac{5a}{81}$$

Solution Steps

Subtract 5 from 1 to get -4.

$$3^{-4}a\times 5$$

Calculate 3 to the power of -4 and get \frac{1}{81}.

$$\frac{1}{81}a\times 5$$

Multiply \frac{1}{81} and 5 to get \frac{5}{81}.

$$\frac{5}{81}a$$

Differentiate w.r.t. a

$$\frac{5}{81} = 0.06172839506172839$$

Steps Using Definition of a Derivative

Subtract 5 from 1 to get -4.

$$\frac{\mathrm{d}}{\mathrm{d}a}(3^{-4}a\times 5)$$

Calculate 3 to the power of -4 and get \frac{1}{81}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{1}{81}a\times 5)$$

Multiply \frac{1}{81} and 5 to get \frac{5}{81}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{5}{81}a)$$

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

$$\frac{5}{81}a^{1-1}$$

Subtract 1 from 1.

$$\frac{5}{81}a^{0}$$

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

$$\frac{5}{81}\times 1$$

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

$$\frac{5}{81}$$