Solve 4u^4v+4u^2v+1

$$4 u ^ { 4 } v + 4 u ^ { 2 } v + 1$$

Differentiate w.r.t. u

$$8uv\left(2u^{2}+1\right)$$

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}.

$$4\times 4vu^{4-1}+2\times 4vu^{2-1}$$

Multiply 4 times 4v.

$$16vu^{4-1}+2\times 4vu^{2-1}$$

Subtract 1 from 4.

$$16vu^{3}+2\times 4vu^{2-1}$$

Multiply 2 times 4v.

$$16vu^{3}+8vu^{2-1}$$

Subtract 1 from 2.

$$16vu^{3}+8vu^{1}$$

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

$$16vu^{3}+8vu$$

Evaluate

$$4vu^{4}+4vu^{2}+1$$