Solve 8abc/4bc+5a-(-4a)=

$$\frac { 8 a b c } { 4 b c } + 5 a - ( - 4 a ) =$$

Evaluate

$$11a$$

Solution Steps

Cancel out 4bc in both numerator and denominator.

$$2a+5a-\left(-4a\right)$$

Combine 2a and 5a to get 7a.

$$7a-\left(-4a\right)$$

The opposite of -4a is 4a.

$$7a+4a$$

Combine 7a and 4a to get 11a.

$$11a$$

Differentiate w.r.t. a

$$11$$

Steps Using Definition of a Derivative

Cancel out 4bc in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}a}(2a+5a-\left(-4a\right))$$

Combine 2a and 5a to get 7a.

$$\frac{\mathrm{d}}{\mathrm{d}a}(7a-\left(-4a\right))$$

The opposite of -4a is 4a.

$$\frac{\mathrm{d}}{\mathrm{d}a}(7a+4a)$$

Combine 7a and 4a to get 11a.

$$\frac{\mathrm{d}}{\mathrm{d}a}(11a)$$

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

$$11a^{1-1}$$

Subtract 1 from 1.

$$11a^{0}$$

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

$$11\times 1$$

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

$$11$$