What is the derivative of R(q)=(q^2+1)^4 ?

The derivative of R(q)=(q^2+1)^4 is 8q(q^2+1)^3

What is the first derivative of R(q)=(q^2+1)^4 ?

The first derivative of R(q)=(q^2+1)^4 is 8q(q^2+1)^3

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derivative of

R (q) = (q^{2} + 1)^{4}

8 q (q^{2} + 1)^{3}

Solution steps

\frac{d}{d q} ((q^{2} + 1)^{4})

Apply the chain rule:

4 (q^{2} + 1)^{3} \frac{d}{d q} (q^{2} + 1)

= 4 (q^{2} + 1)^{3} \frac{d}{d q} (q^{2} + 1)

\frac{d}{d q} (q^{2} + 1) = 2 q

= 4 (q^{2} + 1)^{3} \cdot 2 q

Simplify

= 8 q (q^{2} + 1)^{3}

x \to 3 + lim (\frac{4 x}{x - 3})

y = 8 (x - \frac{1}{x})^{4}, at x = 2

\frac{( x ^{2} - 1 )}{x - 1}

x \to 0 lim (\frac{6 e ^{x} - 6}{x})

\frac{d y}{d x} = \frac{( x ^{2} y - y )}{( y + 1 )}

What is the derivative of R(q)=(q^2+1)^4 ?
The derivative of R(q)=(q^2+1)^4 is 8q(q^2+1)^3
What is the first derivative of R(q)=(q^2+1)^4 ?
The first derivative of R(q)=(q^2+1)^4 is 8q(q^2+1)^3