Solve f(x)=410x+55xdiv22*2+69

$$f(x)=410x+55x \div 22 \times 2+69$$

Evaluate

$$415x+69$$

Solution Steps

Divide 55x by 22 to get \frac{5}{2}x.

$$410x+\frac{5}{2}x\times 2+69$$

Cancel out 2 and 2.

$$410x+5x+69$$

Combine 410x and 5x to get 415x.

$$415x+69$$

Differentiate w.r.t. x

$$415$$

Steps Using Derivative Rule for Sum

Divide 55x by 22 to get \frac{5}{2}x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(410x+\frac{5}{2}x\times 2+69)$$

Cancel out 2 and 2.

$$\frac{\mathrm{d}}{\mathrm{d}x}(410x+5x+69)$$

Combine 410x and 5x to get 415x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(415x+69)$$

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}.

$$415x^{1-1}$$

Subtract 1 from 1.

$$415x^{0}$$

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

$$415\times 1$$

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

$$415$$