Solve 3^2alpha5^2

$$3 ^ { 2 } \alpha 5 ^ { 2 }$$

Evaluate

$$225\alpha$$

Solution Steps

Calculate 3 to the power of 2 and get 9.

$$9\alpha \times 5^{2}$$

Calculate 5 to the power of 2 and get 25.

$$9\alpha \times 25$$

Multiply 9 and 25 to get 225.

$$225\alpha$$

Differentiate w.r.t. α

$$225$$

Steps Using Definition of a Derivative

Calculate 3 to the power of 2 and get 9.

$$\frac{\mathrm{d}}{\mathrm{d}\alpha }(9\alpha \times 5^{2})$$

Calculate 5 to the power of 2 and get 25.

$$\frac{\mathrm{d}}{\mathrm{d}\alpha }(9\alpha \times 25)$$

Multiply 9 and 25 to get 225.

$$\frac{\mathrm{d}}{\mathrm{d}\alpha }(225\alpha )$$

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

$$225\alpha ^{1-1}$$

Subtract 1 from 1.

$$225\alpha ^{0}$$

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

$$225\times 1$$

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

$$225$$