Solve a|-5+481-3(4-1)2-2(4-4)15+103

$$a | - 5 + 481 - 3 ( 4 - 1 ) 2 - 2 ( 4 - 4 ) 15 + 103$$

Evaluate

$$561a$$

Solution Steps

Add -5 and 481 to get 476.

$$a|476-3\left(4-1\right)\times 2-2\left(4-4\right)\times 15+103|$$

Subtract 1 from 4 to get 3.

$$a|476-3\times 3\times 2-2\left(4-4\right)\times 15+103|$$

Multiply 3 and 3 to get 9.

$$a|476-9\times 2-2\left(4-4\right)\times 15+103|$$

Multiply 9 and 2 to get 18.

$$a|476-18-2\left(4-4\right)\times 15+103|$$

Subtract 18 from 476 to get 458.

$$a|458-2\left(4-4\right)\times 15+103|$$

Subtract 4 from 4 to get 0.

$$a|458-2\times 0\times 15+103|$$

Multiply 2 and 0 to get 0.

$$a|458-0\times 15+103|$$

Multiply 0 and 15 to get 0.

$$a|458-0+103|$$

Subtract 0 from 458 to get 458.

$$a|458+103|$$

Add 458 and 103 to get 561.

$$a|561|$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of 561 is 561.

$$a\times 561$$

Differentiate w.r.t. a

$$561$$

Steps Using Definition of a Derivative

Add -5 and 481 to get 476.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a|476-3\left(4-1\right)\times 2-2\left(4-4\right)\times 15+103|)$$

Subtract 1 from 4 to get 3.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a|476-3\times 3\times 2-2\left(4-4\right)\times 15+103|)$$

Multiply 3 and 3 to get 9.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a|476-9\times 2-2\left(4-4\right)\times 15+103|)$$

Multiply 9 and 2 to get 18.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a|476-18-2\left(4-4\right)\times 15+103|)$$

Subtract 18 from 476 to get 458.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a|458-2\left(4-4\right)\times 15+103|)$$

Subtract 4 from 4 to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a|458-2\times 0\times 15+103|)$$

Multiply 2 and 0 to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a|458-0\times 15+103|)$$

Multiply 0 and 15 to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a|458-0+103|)$$

Subtract 0 from 458 to get 458.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a|458+103|)$$

Add 458 and 103 to get 561.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a|561|)$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of 561 is 561.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a\times 561)$$

The derivative of ax^{n} is nax^{n-1}.

$$561a^{1-1}$$

Subtract 1 from 1.

$$561a^{0}$$

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

$$561\times 1$$

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

$$561$$