Solve (12r+3)+(5+3r^4)

$$( 12 r + 3 ) + ( 5 + 3 r ^ { 4 } )$$

Differentiate w.r.t. r

$$12\left(r^{3}+1\right)$$

Steps Using Derivative Rule for Sum

Add 3 and 5 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}r}(12r+8+3r^{4})$$

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}.

$$12r^{1-1}+4\times 3r^{4-1}$$

Subtract 1 from 1.

$$12r^{0}+4\times 3r^{4-1}$$

Multiply 4 times 3.

$$12r^{0}+12r^{4-1}$$

Subtract 1 from 4.

$$12r^{0}+12r^{3}$$

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

$$12\times 1+12r^{3}$$

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

$$12+12r^{3}$$

Evaluate

$$3r^{4}+12r+8$$

Solution Steps

Add 3 and 5 to get 8.

$$12r+8+3r^{4}$$