Solve (8h^3+2h^2+3h+5)+(h^3+7h)

$$( 8 h ^ { 3 } + 2 h ^ { 2 } + 3 h + 5 ) + ( h ^ { 3 } + 7 h )$$

Evaluate

$$9h^{3}+2h^{2}+10h+5$$

Solution Steps

Combine 8h^{3} and h^{3} to get 9h^{3}.

$$9h^{3}+2h^{2}+3h+5+7h$$

Combine 3h and 7h to get 10h.

$$9h^{3}+2h^{2}+10h+5$$

Differentiate w.r.t. h

$$27h^{2}+4h+10$$

Steps Using Derivative Rule for Sum

Combine 8h^{3} and h^{3} to get 9h^{3}.

$$\frac{\mathrm{d}}{\mathrm{d}h}(9h^{3}+2h^{2}+3h+5+7h)$$

Combine 3h and 7h to get 10h.

$$\frac{\mathrm{d}}{\mathrm{d}h}(9h^{3}+2h^{2}+10h+5)$$

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}.

$$3\times 9h^{3-1}+2\times 2h^{2-1}+10h^{1-1}$$

Multiply 3 times 9.

$$27h^{3-1}+2\times 2h^{2-1}+10h^{1-1}$$

Subtract 1 from 3.

$$27h^{2}+2\times 2h^{2-1}+10h^{1-1}$$

Multiply 2 times 2.

$$27h^{2}+4h^{2-1}+10h^{1-1}$$

Subtract 1 from 2.

$$27h^{2}+4h^{1}+10h^{1-1}$$

Subtract 1 from 1.

$$27h^{2}+4h^{1}+10h^{0}$$

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

$$27h^{2}+4h+10h^{0}$$

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

$$27h^{2}+4h+10\times 1$$

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

$$27h^{2}+4h+10$$