Solve y-3^2-24div(-2)^3

$$y - 3 ^ { 2 } - 24 \div ( - 2 ) ^ { 3 }$$

Evaluate

$$y-6$$

Solution Steps

Calculate 3 to the power of 2 and get 9.

$$y-9-\frac{24}{\left(-2\right)^{3}}$$

Calculate -2 to the power of 3 and get -8.

$$y-9-\frac{24}{-8}$$

Divide 24 by -8 to get -3.

$$y-9-\left(-3\right)$$

The opposite of -3 is 3.

$$y-9+3$$

Add -9 and 3 to get -6.

$$y-6$$

Differentiate w.r.t. y

$$1$$

Steps Using Derivative Rule for Sum

Calculate 3 to the power of 2 and get 9.

$$\frac{\mathrm{d}}{\mathrm{d}y}(y-9-\frac{24}{\left(-2\right)^{3}})$$

Calculate -2 to the power of 3 and get -8.

$$\frac{\mathrm{d}}{\mathrm{d}y}(y-9-\frac{24}{-8})$$

Divide 24 by -8 to get -3.

$$\frac{\mathrm{d}}{\mathrm{d}y}(y-9-\left(-3\right))$$

The opposite of -3 is 3.

$$\frac{\mathrm{d}}{\mathrm{d}y}(y-9+3)$$

Add -9 and 3 to get -6.

$$\frac{\mathrm{d}}{\mathrm{d}y}(y-6)$$

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}.

$$y^{1-1}$$

Subtract 1 from 1.

$$y^{0}$$

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

$$1$$