Solve b^2*5^4/5^2

$$\frac { b ^ { 2 } \cdot 5 ^ { 4 } } { 5 ^ { 2 } }$$

Evaluate

$$25b^{2}$$

Solution Steps

Cancel out 5^{2} in both numerator and denominator.

$$5^{2}b^{2}$$

Calculate 5 to the power of 2 and get 25.

$$25b^{2}$$

Differentiate w.r.t. b

$$50b$$

Steps Using Definition of a Derivative

Cancel out 5^{2} in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}b}(5^{2}b^{2})$$

Calculate 5 to the power of 2 and get 25.

$$\frac{\mathrm{d}}{\mathrm{d}b}(25b^{2})$$

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

$$2\times 25b^{2-1}$$

Multiply 2 times 25.

$$50b^{2-1}$$

Subtract 1 from 2.

$$50b^{1}$$

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

$$50b$$