Solve x+37*3+38*7+39*6+42*1+44*1)=

$$x + 37 \times 3 + 38 \times 7 + 39 \times 6 + 42 \times 1 + 44 \times 1 ) =$$

Evaluate

$$x+697$$

Solution Steps

Multiply 37 and 3 to get 111. Multiply 38 and 7 to get 266. Multiply 39 and 6 to get 234. Multiply 42 and 1 to get 42. Multiply 44 and 1 to get 44.

$$x+111+266+234+42+44$$

Add 111 and 266 to get 377.

$$x+377+234+42+44$$

Add 377 and 234 to get 611.

$$x+611+42+44$$

Add 611 and 42 to get 653.

$$x+653+44$$

Add 653 and 44 to get 697.

$$x+697$$

Differentiate w.r.t. x

$$1$$

Steps Using Derivative Rule for Sum

Multiply 37 and 3 to get 111. Multiply 38 and 7 to get 266. Multiply 39 and 6 to get 234. Multiply 42 and 1 to get 42. Multiply 44 and 1 to get 44.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x+111+266+234+42+44)$$

Add 111 and 266 to get 377.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x+377+234+42+44)$$

Add 377 and 234 to get 611.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x+611+42+44)$$

Add 611 and 42 to get 653.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x+653+44)$$

Add 653 and 44 to get 697.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x+697)$$

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}.

$$x^{1-1}$$

Subtract 1 from 1.

$$x^{0}$$

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

$$1$$