Solve 6h^{2}-3h^3+10-5h^2+2h^3-h^2

$$6 h ^ { 2 } - 3 h ^ { 3 } + 10 - 5 h ^ { 2 } + 2 h ^ { 3 } - h ^ { 2 }$$

Evaluate

$$10-h^{3}$$

Solution Steps

Combine 6h^{2} and -5h^{2} to get h^{2}.

$$h^{2}-3h^{3}+10+2h^{3}-h^{2}$$

Combine -3h^{3} and 2h^{3} to get -h^{3}.

$$h^{2}-h^{3}+10-h^{2}$$

Combine h^{2} and -h^{2} to get 0.

$$-h^{3}+10$$

Differentiate w.r.t. h

$$-3h^{2}$$

Steps Using Derivative Rule for Sum

Combine 6h^{2} and -5h^{2} to get h^{2}.

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

Combine -3h^{3} and 2h^{3} to get -h^{3}.

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

Combine h^{2} and -h^{2} to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}h}(-h^{3}+10)$$

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}.

$$3\left(-1\right)h^{3-1}$$

Multiply 3 times -1.

$$-3h^{3-1}$$

Subtract 1 from 3.

$$-3h^{2}$$