Solve (5w-5w^3)+(9w^3-9+9w)

$$( 5 w - 5 w ^ { 3 } ) + ( 9 w ^ { 3 } - 9 + 9 w )$$

Evaluate

$$4w^{3}+14w-9$$

Solution Steps

Combine -5w^{3} and 9w^{3} to get 4w^{3}.

$$5w+4w^{3}-9+9w$$

Combine 5w and 9w to get 14w.

$$14w+4w^{3}-9$$

Differentiate w.r.t. w

$$12w^{2}+14$$

Steps Using Derivative Rule for Sum

Combine -5w^{3} and 9w^{3} to get 4w^{3}.

$$\frac{\mathrm{d}}{\mathrm{d}w}(5w+4w^{3}-9+9w)$$

Combine 5w and 9w to get 14w.

$$\frac{\mathrm{d}}{\mathrm{d}w}(14w+4w^{3}-9)$$

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}.

$$14w^{1-1}+3\times 4w^{3-1}$$

Subtract 1 from 1.

$$14w^{0}+3\times 4w^{3-1}$$

Multiply 3 times 4.

$$14w^{0}+12w^{3-1}$$

Subtract 1 from 3.

$$14w^{0}+12w^{2}$$

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

$$14\times 1+12w^{2}$$

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

$$14+12w^{2}$$