Solve (-7w^5-3w^3-4)+(-9w^5-7w^3+2w-5)

$$( - 7 w ^ { 5 } - 3 w ^ { 3 } - 4 ) + ( - 9 w ^ { 5 } - 7 w ^ { 3 } + 2 w - 5 )$$

Evaluate

$$-16w^{5}-10w^{3}+2w-9$$

Solution Steps

Combine -7w^{5} and -9w^{5} to get -16w^{5}.

$$-16w^{5}-3w^{3}-4-7w^{3}+2w-5$$

Combine -3w^{3} and -7w^{3} to get -10w^{3}.

$$-16w^{5}-10w^{3}-4+2w-5$$

Subtract 5 from -4 to get -9.

$$-16w^{5}-10w^{3}-9+2w$$

Differentiate w.r.t. w

$$2-30w^{2}-80w^{4}$$

Steps Using Derivative Rule for Sum

Combine -7w^{5} and -9w^{5} to get -16w^{5}.

$$\frac{\mathrm{d}}{\mathrm{d}w}(-16w^{5}-3w^{3}-4-7w^{3}+2w-5)$$

Combine -3w^{3} and -7w^{3} to get -10w^{3}.

$$\frac{\mathrm{d}}{\mathrm{d}w}(-16w^{5}-10w^{3}-4+2w-5)$$

Subtract 5 from -4 to get -9.

$$\frac{\mathrm{d}}{\mathrm{d}w}(-16w^{5}-10w^{3}-9+2w)$$

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}.

$$5\left(-16\right)w^{5-1}+3\left(-10\right)w^{3-1}+2w^{1-1}$$

Multiply 5 times -16.

$$-80w^{5-1}+3\left(-10\right)w^{3-1}+2w^{1-1}$$

Subtract 1 from 5.

$$-80w^{4}+3\left(-10\right)w^{3-1}+2w^{1-1}$$

Multiply 3 times -10.

$$-80w^{4}-30w^{3-1}+2w^{1-1}$$

Subtract 1 from 3.

$$-80w^{4}-30w^{2}+2w^{1-1}$$

Subtract 1 from 1.

$$-80w^{4}-30w^{2}+2w^{0}$$

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

$$-80w^{4}-30w^{2}+2\times 1$$

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

$$-80w^{4}-30w^{2}+2$$