Solve E(x)=9*0.056+10*0.542*11x

$$E ( x ) = 9 \times 0.056 + 10 \times 0.542 \times 11 x$$

Evaluate

$$\frac{2981x}{50}+0.504$$

Solution Steps

Multiply 9 and 0.056 to get 0.504.

$$0.504+10\times 0.542\times 11x$$

Multiply 10 and 0.542 to get 5.42.

$$0.504+5.42\times 11x$$

Multiply 5.42 and 11 to get 59.62.

$$0.504+59.62x$$

Differentiate w.r.t. x

$$59.62$$

Steps Using Derivative Rule for Sum

Multiply 9 and 0.056 to get 0.504.

$$\frac{\mathrm{d}}{\mathrm{d}x}(0.504+10\times 0.542\times 11x)$$

Multiply 10 and 0.542 to get 5.42.

$$\frac{\mathrm{d}}{\mathrm{d}x}(0.504+5.42\times 11x)$$

Multiply 5.42 and 11 to get 59.62.

$$\frac{\mathrm{d}}{\mathrm{d}x}(0.504+59.62x)$$

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}.

$$59.62x^{1-1}$$

Subtract 1 from 1.

$$59.62x^{0}$$

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

$$59.62\times 1$$

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

$$59.62$$