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Popular >

derivative of (a-xsqrt(a+x))

Solution

\frac{d}{d x} ((a - x) a + x)

Solution

\frac{- 3 x - a}{2 a + x}

Solution steps

\frac{d}{d x} ((a - x) a + x)

Apply the Product Rule:

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

f = a - x, g = a + x

= \frac{d}{d x} (a - x) a + x + \frac{d}{d x} (a + x) (a - x)

\frac{d}{d x} (a - x) = - 1

\frac{d}{d x} (a + x) = \frac{1}{2 a + x}

= (- 1) a + x + \frac{1}{2 a + x} (a - x)

Simplify

(- 1) a + x + \frac{1}{2 a + x} (a - x) : \frac{- 3 x - a}{2 a + x}

= \frac{- 3 x - a}{2 a + x}

Popular Examples

derivative of e^{2x}cos(pix)

\frac{d}{d x} (e^{2 x} cos (π x))

integral of sin(ln(8x))

\int sin (ln (8 x)) d x

derivative of arcsin(x)derivative of

arcsin (x)

(d^2y)/(dx^2)+2/x (dy)/(dx)=3xx

\frac{d ^{2} y}{d x ^{2}} + \frac{2}{x} \frac{d y}{d x} = 3 xx

tangent of f(x)=(x^2+7)(5x+4),\at x=2 tangent of

f (x) = (x^{2} + 7) (5 x + 4), at x = 2

Frequently Asked Questions (FAQ)

What is the derivative of (a-xsqrt(a+x)) ?
The derivative of (a-xsqrt(a+x)) is (-3x-a)/(2sqrt(a+x))
What is the first derivative of (a-xsqrt(a+x)) ?
The first derivative of (a-xsqrt(a+x)) is (-3x-a)/(2sqrt(a+x))