Solve sqrt{25}*3^2+5y

$$\sqrt { 25 } \cdot 3 ^ { 2 } + 5 y$$

Evaluate

$$5\left(y+9\right)$$

Solution Steps

Calculate the square root of 25 and get 5.

$$5\times 3^{2}+5y$$

Calculate 3 to the power of 2 and get 9.

$$5\times 9+5y$$

Multiply 5 and 9 to get 45.

$$45+5y$$

Differentiate w.r.t. y

$$5$$

Steps Using Derivative Rule for Sum

Calculate the square root of 25 and get 5.

$$\frac{\mathrm{d}}{\mathrm{d}y}(5\times 3^{2}+5y)$$

Calculate 3 to the power of 2 and get 9.

$$\frac{\mathrm{d}}{\mathrm{d}y}(5\times 9+5y)$$

Multiply 5 and 9 to get 45.

$$\frac{\mathrm{d}}{\mathrm{d}y}(45+5y)$$

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$5y^{1-1}$$

Subtract 1 from 1.

$$5y^{0}$$

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

$$5\times 1$$

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

$$5$$