Solve 28w+6+5w^6-6w^4

$$28w+6+5 { w }^{ 6 } -6 { w }^{ 4 }$$

Differentiate w.r.t. w

$$30w^{5}-24w^{3}+28$$

Steps Using Derivative Rule for Sum

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}.

$$28w^{1-1}+6\times 5w^{6-1}+4\left(-6\right)w^{4-1}$$

Subtract 1 from 1.

$$28w^{0}+6\times 5w^{6-1}+4\left(-6\right)w^{4-1}$$

Multiply 6 times 5.

$$28w^{0}+30w^{6-1}+4\left(-6\right)w^{4-1}$$

Subtract 1 from 6.

$$28w^{0}+30w^{5}+4\left(-6\right)w^{4-1}$$

Multiply 6 times 5.

$$28w^{0}+30w^{5}-24w^{4-1}$$

Subtract 1 from 4.

$$28w^{0}+30w^{5}-24w^{3}$$

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

$$28\times 1+30w^{5}-24w^{3}$$

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

$$28+30w^{5}-24w^{3}$$

Evaluate

$$5w^{6}-6w^{4}+28w+6$$