Solve a*5^2-a*2^2

$$a \times 5 ^ { 2 } - a \times 2 ^ { 2 }$$

Evaluate

$$21a$$

Solution Steps

Calculate 5 to the power of 2 and get 25.

$$a\times 25-a\times 2^{2}$$

Calculate 2 to the power of 2 and get 4.

$$a\times 25-a\times 4$$

Combine a\times 25 and -a\times 4 to get 21a.

$$21a$$

Differentiate w.r.t. a

$$21$$

Steps Using Definition of a Derivative

Calculate 5 to the power of 2 and get 25.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a\times 25-a\times 2^{2})$$

Calculate 2 to the power of 2 and get 4.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a\times 25-a\times 4)$$

Combine a\times 25 and -a\times 4 to get 21a.

$$\frac{\mathrm{d}}{\mathrm{d}a}(21a)$$

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

$$21a^{1-1}$$

Subtract 1 from 1.

$$21a^{0}$$

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

$$21\times 1$$

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

$$21$$