Solve 7r^2+4+2r^2+1

$$7 r ^ { 2 } + 4 + 2 r ^ { 2 } + 1$$

Evaluate

$$9r^{2}+5$$

Solution Steps

Combine 7r^{2} and 2r^{2} to get 9r^{2}.

$$9r^{2}+4+1$$

Add 4 and 1 to get 5.

$$9r^{2}+5$$

Differentiate w.r.t. r

$$18r$$

Steps Using Derivative Rule for Sum

Combine 7r^{2} and 2r^{2} to get 9r^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}r}(9r^{2}+4+1)$$

Add 4 and 1 to get 5.

$$\frac{\mathrm{d}}{\mathrm{d}r}(9r^{2}+5)$$

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}.

$$2\times 9r^{2-1}$$

Multiply 2 times 9.

$$18r^{2-1}$$

Subtract 1 from 2.

$$18r^{1}$$

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

$$18r$$