What is the derivative of sqrt(9+x+y^2) ?

The derivative of sqrt(9+x+y^2) is (2y\frac{dy)/(dx)+1}{2sqrt(9+x+y^2)}

What is the first derivative of sqrt(9+x+y^2) ?

The first derivative of sqrt(9+x+y^2) is (2y\frac{dy)/(dx)+1}{2sqrt(9+x+y^2)}

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\frac{d}{d x} (9 + x + y^{2})

\frac{2 y \frac{d y}{d x} + 1}{2 9 + x + y ^{2}}

Solution steps

\frac{d}{d x} (9 + x + y^{2})

Apply the chain rule:

\frac{1}{2 9 + x + y ^{2}} \frac{d}{d x} (9 + x + y^{2})

= \frac{1}{2 9 + x + y ^{2}} \frac{d}{d x} (9 + x + y^{2})

\frac{d}{d x} (9 + x + y^{2}) = 2 y \frac{d y}{d x} + 1

= \frac{1}{2 9 + x + y ^{2}} (2 y \frac{d y}{d x} + 1)

Simplify

\frac{1}{2 9 + x + y ^{2}} (2 y \frac{d y}{d x} + 1) : \frac{2 y \frac{d y}{d x} + 1}{2 9 + x + y ^{2}}

= \frac{2 y \frac{d y}{d x} + 1}{2 9 + x + y ^{2}}

\int x^{13} sin (x^{14}) d x

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

\frac{d}{d x} (x^{4} - 2 x)

y^{^{'}} = 0.1 ln (\frac{4000}{y}) y

\int t e^{- 9 t} d t

What is the derivative of sqrt(9+x+y^2) ?
The derivative of sqrt(9+x+y^2) is (2y\frac{dy)/(dx)+1}{2sqrt(9+x+y^2)}
What is the first derivative of sqrt(9+x+y^2) ?
The first derivative of sqrt(9+x+y^2) is (2y\frac{dy)/(dx)+1}{2sqrt(9+x+y^2)}