What is the derivative of xsqrt(x+9) ?

The derivative of xsqrt(x+9) is (3x+18)/(2sqrt(x+9))

What is the first derivative of xsqrt(x+9) ?

The first derivative of xsqrt(x+9) is (3x+18)/(2sqrt(x+9))

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\frac{d}{d x} (x x + 9)

\frac{3 x + 18}{2 x + 9}

Solution steps

\frac{d}{d x} (x x + 9)

Apply the Product Rule:

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

f = x, g = x + 9

= \frac{d x}{d x} x + 9 + \frac{d}{d x} (x + 9) x

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

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

= 1 \cdot x + 9 + \frac{1}{2 x + 9} x

Simplify

1 \cdot x + 9 + \frac{1}{2 x + 9} x : \frac{3 x + 18}{2 x + 9}

= \frac{3 x + 18}{2 x + 9}

\frac{9}{4} t^{2} e^{5 t}

\int \frac{4 x - 1}{x ^{2} + x - 2} d x

x \to c lim ((8)^{\frac{2}{3}})

x \to 1 - lim (7 ∣ x + 1 ∣ - 4)

\int \frac{4}{3} x^{2} d x

What is the derivative of xsqrt(x+9) ?
The derivative of xsqrt(x+9) is (3x+18)/(2sqrt(x+9))
What is the first derivative of xsqrt(x+9) ?
The first derivative of xsqrt(x+9) is (3x+18)/(2sqrt(x+9))