What is the derivative of axsqrt(a+x) ?

The derivative of axsqrt(a+x) is (a(3x+2a))/(2sqrt(a+x))

What is the first derivative of axsqrt(a+x) ?

The first derivative of axsqrt(a+x) is (a(3x+2a))/(2sqrt(a+x))

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

\frac{a ( 3 x + 2 a )}{2 a + x}

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

f = x, g = a + x

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

\frac{d x}{d x} = 1

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

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

Simplify

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

= \frac{a ( 3 x + 2 a )}{2 a + x}

f (x) = tan (x^{2})

x \to - 4 lim (\frac{x ^{2}}{4 - x})

y^{^{''}} - 2 y^{^{'}} - 3 y = 4 e^{- x}, y (0) = 4, y^{^{'}} (0) = - 1

\int \frac{x ^{2} + 8}{x ^{2}} d x

\frac{d}{d x} (x (x^{2} - 5)^{\frac{1}{3}})

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