What is the derivative of arctan(6y^5+1) ?

The derivative of arctan(6y^5+1) is (15y^4)/(18y^{10)+6y^5+1}

What is the first derivative of arctan(6y^5+1) ?

The first derivative of arctan(6y^5+1) is (15y^4)/(18y^{10)+6y^5+1}

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derivative of

arctan (6 y^{5} + 1)

\frac{15 y ^{4}}{18 y ^{10} + 6 y ^{5} + 1}

Solution steps

\frac{d}{d y} (arctan (6 y^{5} + 1))

Apply the chain rule:

\frac{1}{( 6 y ^{5} + 1 ) ^{2} + 1} \frac{d}{d y} (6 y^{5} + 1)

= \frac{1}{( 6 y ^{5} + 1 ) ^{2} + 1} \frac{d}{d y} (6 y^{5} + 1)

\frac{d}{d y} (6 y^{5} + 1) = 30 y^{4}

= \frac{1}{( 6 y ^{5} + 1 ) ^{2} + 1} \cdot 30 y^{4}

Simplify

\frac{1}{( 6 y ^{5} + 1 ) ^{2} + 1} \cdot 30 y^{4} : \frac{15 y ^{4}}{18 y ^{10} + 6 y ^{5} + 1}

= \frac{15 y ^{4}}{18 y ^{10} + 6 y ^{5} + 1}

\frac{\partial}{\partial x} (y^{2} cos (y x))

\int 2 x x - 1 d x

\frac{d}{d x} (x (3 - 2 x)^{5})

y^{^{''}} + 4 y = t^{2} e^{3 t} + 3

x y^{^{'}} = y^{2} + 1

What is the derivative of arctan(6y^5+1) ?
The derivative of arctan(6y^5+1) is (15y^4)/(18y^{10)+6y^5+1}
What is the first derivative of arctan(6y^5+1) ?
The first derivative of arctan(6y^5+1) is (15y^4)/(18y^{10)+6y^5+1}