Solve 5a+90+100-14*18-6a-76*61*75

$$5 a + 90 + 100 - 14 \cdot 18 - 6 a - 76 \cdot 61 \cdot 75$$

Evaluate

$$-a-347762$$

Solution Steps

Add 90 and 100 to get 190.

$$5a+190-14\times 18-6a-76\times 61\times 75$$

Multiply 14 and 18 to get 252.

$$5a+190-252-6a-76\times 61\times 75$$

Subtract 252 from 190 to get -62.

$$5a-62-6a-76\times 61\times 75$$

Combine 5a and -6a to get -a.

$$-a-62-76\times 61\times 75$$

Multiply 76 and 61 to get 4636.

$$-a-62-4636\times 75$$

Multiply 4636 and 75 to get 347700.

$$-a-62-347700$$

Subtract 347700 from -62 to get -347762.

$$-a-347762$$

Differentiate w.r.t. a

$$-1$$

Steps Using Derivative Rule for Sum

Add 90 and 100 to get 190.

$$\frac{\mathrm{d}}{\mathrm{d}a}(5a+190-14\times 18-6a-76\times 61\times 75)$$

Multiply 14 and 18 to get 252.

$$\frac{\mathrm{d}}{\mathrm{d}a}(5a+190-252-6a-76\times 61\times 75)$$

Subtract 252 from 190 to get -62.

$$\frac{\mathrm{d}}{\mathrm{d}a}(5a-62-6a-76\times 61\times 75)$$

Combine 5a and -6a to get -a.

$$\frac{\mathrm{d}}{\mathrm{d}a}(-a-62-76\times 61\times 75)$$

Multiply 76 and 61 to get 4636.

$$\frac{\mathrm{d}}{\mathrm{d}a}(-a-62-4636\times 75)$$

Multiply 4636 and 75 to get 347700.

$$\frac{\mathrm{d}}{\mathrm{d}a}(-a-62-347700)$$

Subtract 347700 from -62 to get -347762.

$$\frac{\mathrm{d}}{\mathrm{d}a}(-a-347762)$$

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}.

$$-a^{1-1}$$

Subtract 1 from 1.

$$-a^{0}$$

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

$$-1$$