What is the derivative of sqrt(y-x)n(y+x) ?

The derivative of sqrt(y-x)n(y+x) is (n(-x\frac{dy)/(dx)-3x+3y(dy)/(dx)+y)}{2sqrt(y-x)}

What is the first derivative of sqrt(y-x)n(y+x) ?

The first derivative of sqrt(y-x)n(y+x) is (n(-x\frac{dy)/(dx)-3x+3y(dy)/(dx)+y)}{2sqrt(y-x)}

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Popular >

\frac{d}{d x} (y - x n (y + x))

\frac{n ( - x \frac{d y}{d x} - 3 x + 3 y \frac{d y}{d x} + y )}{2 y - x}

Solution steps

\frac{d}{d x} (y - x n (y + x))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= n \frac{d}{d x} (y - x (y + x))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = y - x, g = y + x

= n (\frac{d}{d x} (y - x) (y + x) + \frac{d}{d x} (y + x) y - x)

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

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

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

Simplify

n (\frac{\frac{d y}{d x} - 1}{2 y - x} (y + x) + (\frac{d y}{d x} + 1) y - x) : \frac{n ( - x \frac{d y}{d x} - 3 x + 3 y \frac{d y}{d x} + y )}{2 y - x}

= \frac{n ( - x \frac{d y}{d x} - 3 x + 3 y \frac{d y}{d x} + y )}{2 y - x}

\frac{\partial}{\partial y} (x - y - 1)

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

\frac{d ^{2}}{d x ^{2}} (sec (x))

e^{e^{x}} \to 0 + lim (\frac{e ^{e^{x} - 2}}{e ^{e^{x}}})

(x - 1) (x^{2} - 8 x + 7)

What is the derivative of sqrt(y-x)n(y+x) ?
The derivative of sqrt(y-x)n(y+x) is (n(-x\frac{dy)/(dx)-3x+3y(dy)/(dx)+y)}{2sqrt(y-x)}
What is the first derivative of sqrt(y-x)n(y+x) ?
The first derivative of sqrt(y-x)n(y+x) is (n(-x\frac{dy)/(dx)-3x+3y(dy)/(dx)+y)}{2sqrt(y-x)}