Solve 30-{s[(6-3)^2+2(sqrt{100}div5)]+30}

$$30 - \{ s [ ( 6 - 3 ) ^ { 2 } + 2 ( \sqrt { 100 } \div 5 ) ] + 30 \}$$

Evaluate

$$-13s$$

Solution Steps

Subtract 3 from 6 to get 3.

$$30-\left(s\left(3^{2}+2\times \frac{\sqrt{100}}{5}\right)+30\right)$$

Calculate 3 to the power of 2 and get 9.

$$30-\left(s\left(9+2\times \frac{\sqrt{100}}{5}\right)+30\right)$$

Calculate the square root of 100 and get 10.

$$30-\left(s\left(9+2\times \frac{10}{5}\right)+30\right)$$

Divide 10 by 5 to get 2.

$$30-\left(s\left(9+2\times 2\right)+30\right)$$

Multiply 2 and 2 to get 4.

$$30-\left(s\left(9+4\right)+30\right)$$

Add 9 and 4 to get 13.

$$30-\left(s\times 13+30\right)$$

To find the opposite of s\times 13+30, find the opposite of each term.

$$30-s\times 13-30$$

Multiply -1 and 13 to get -13.

$$30-13s-30$$

Subtract 30 from 30 to get 0.

$$-13s$$

Differentiate w.r.t. s

$$-13$$

Steps Using Definition of a Derivative

Subtract 3 from 6 to get 3.

$$\frac{\mathrm{d}}{\mathrm{d}s}(30-\left(s\left(3^{2}+2\times \frac{\sqrt{100}}{5}\right)+30\right))$$

Calculate 3 to the power of 2 and get 9.

$$\frac{\mathrm{d}}{\mathrm{d}s}(30-\left(s\left(9+2\times \frac{\sqrt{100}}{5}\right)+30\right))$$

Calculate the square root of 100 and get 10.

$$\frac{\mathrm{d}}{\mathrm{d}s}(30-\left(s\left(9+2\times \frac{10}{5}\right)+30\right))$$

Divide 10 by 5 to get 2.

$$\frac{\mathrm{d}}{\mathrm{d}s}(30-\left(s\left(9+2\times 2\right)+30\right))$$

Multiply 2 and 2 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}s}(30-\left(s\left(9+4\right)+30\right))$$

Add 9 and 4 to get 13.

$$\frac{\mathrm{d}}{\mathrm{d}s}(30-\left(s\times 13+30\right))$$

To find the opposite of s\times 13+30, find the opposite of each term.

$$\frac{\mathrm{d}}{\mathrm{d}s}(30-s\times 13-30)$$

Multiply -1 and 13 to get -13.

$$\frac{\mathrm{d}}{\mathrm{d}s}(30-13s-30)$$

Subtract 30 from 30 to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}s}(-13s)$$

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

$$-13s^{1-1}$$

Subtract 1 from 1.

$$-13s^{0}$$

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

$$-13$$