Solve 60+0.7*0.8y+370+600+470-0.06y

$$60 + 0.7 \times 0.8 y + 370 + 600 + 470 - 0.06 y$$

Evaluate

$$\frac{y}{2}+1500$$

Solution Steps

Multiply 0.7 and 0.8 to get 0.56.

$$60+0.56y+370+600+470-0.06y$$

Add 60 and 370 to get 430.

$$430+0.56y+600+470-0.06y$$

Add 430 and 600 to get 1030.

$$1030+0.56y+470-0.06y$$

Add 1030 and 470 to get 1500.

$$1500+0.56y-0.06y$$

Combine 0.56y and -0.06y to get 0.5y.

$$1500+0.5y$$

Differentiate w.r.t. y

$$0.5$$

Steps Using Derivative Rule for Sum

Multiply 0.7 and 0.8 to get 0.56.

$$\frac{\mathrm{d}}{\mathrm{d}y}(60+0.56y+370+600+470-0.06y)$$

Add 60 and 370 to get 430.

$$\frac{\mathrm{d}}{\mathrm{d}y}(430+0.56y+600+470-0.06y)$$

Add 430 and 600 to get 1030.

$$\frac{\mathrm{d}}{\mathrm{d}y}(1030+0.56y+470-0.06y)$$

Add 1030 and 470 to get 1500.

$$\frac{\mathrm{d}}{\mathrm{d}y}(1500+0.56y-0.06y)$$

Combine 0.56y and -0.06y to get 0.5y.

$$\frac{\mathrm{d}}{\mathrm{d}y}(1500+0.5y)$$

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}.

$$0.5y^{1-1}$$

Subtract 1 from 1.

$$0.5y^{0}$$

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

$$0.5\times 1$$

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

$$0.5$$