Solve (5w^3-w+2w^2+4)+(3w^2+1-4

$$( 5 w ^ { 3 } - w + 2 w ^ { 2 } + 4 ) + ( 3 w ^ { 2 } + 1 - 4$$

Evaluate

$$5w^{3}+5w^{2}-w+1$$

Solution Steps

Combine 2w^{2} and 3w^{2} to get 5w^{2}.

$$5w^{3}-w+5w^{2}+4+1-4$$

Add 4 and 1 to get 5.

$$5w^{3}-w+5w^{2}+5-4$$

Subtract 4 from 5 to get 1.

$$5w^{3}-w+5w^{2}+1$$

Differentiate w.r.t. w

$$15w^{2}+10w-1$$

Steps Using Derivative Rule for Sum

Combine 2w^{2} and 3w^{2} to get 5w^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}w}(5w^{3}-w+5w^{2}+4+1-4)$$

Add 4 and 1 to get 5.

$$\frac{\mathrm{d}}{\mathrm{d}w}(5w^{3}-w+5w^{2}+5-4)$$

Subtract 4 from 5 to get 1.

$$\frac{\mathrm{d}}{\mathrm{d}w}(5w^{3}-w+5w^{2}+1)$$

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}.

$$3\times 5w^{3-1}-w^{1-1}+2\times 5w^{2-1}$$

Multiply 3 times 5.

$$15w^{3-1}-w^{1-1}+2\times 5w^{2-1}$$

Subtract 1 from 3.

$$15w^{2}-w^{1-1}+2\times 5w^{2-1}$$

Subtract 1 from 1.

$$15w^{2}-w^{0}+2\times 5w^{2-1}$$

Multiply 1 times -1.

$$15w^{2}-w^{0}+10w^{2-1}$$

Subtract 1 from 2.

$$15w^{2}-w^{0}+10w^{1}$$

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

$$15w^{2}-w^{0}+10w$$

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

$$15w^{2}-1+10w$$