What is the derivative of ((sqrt(x)/3+1)^{3/2}) ?

The derivative of ((sqrt(x)/3+1)^{3/2}) is ((sqrt(x)+3)^{1/2})/(4*3^{1/2)x^{1/2}}

What is the first derivative of ((sqrt(x)/3+1)^{3/2}) ?

The first derivative of ((sqrt(x)/3+1)^{3/2}) is ((sqrt(x)+3)^{1/2})/(4*3^{1/2)x^{1/2}}

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

\frac{( x + 3 ) ^{\frac{1}{2}}}{4 \cdot 3 ^{\frac{1}{2}} x ^{\frac{1}{2}}}

Solution steps

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

Simplify

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

= \frac{d}{d x} ((\frac{x + 3}{3})^{\frac{3}{2}})

Apply the chain rule:

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

= \frac{3 ( \frac{x + 3}{3} ) ^{\frac{1}{2}}}{2} \frac{d}{d x} (\frac{x + 3}{3})

\frac{d}{d x} (\frac{x + 3}{3}) = \frac{1}{6 x ^{\frac{1}{2}}}

= \frac{3 ( \frac{x + 3}{3} ) ^{\frac{1}{2}}}{2} \cdot \frac{1}{6 x ^{\frac{1}{2}}}

Simplify

\frac{3 ( \frac{x + 3}{3} ) ^{\frac{1}{2}}}{2} \cdot \frac{1}{6 x ^{\frac{1}{2}}} : \frac{( x + 3 ) ^{\frac{1}{2}}}{4 \cdot 3 ^{\frac{1}{2}} x ^{\frac{1}{2}}}

= \frac{( x + 3 ) ^{\frac{1}{2}}}{4 \cdot 3 ^{\frac{1}{2}} x ^{\frac{1}{2}}}

\int cos (x) (6 + 4 sin^{2} (x)) d x

\frac{\partial}{\partial x} (9 - 3 x^{2} - y^{2})

x \to 2 lim (3 - x^{2})

n = 0 \sum \infty 3

What is the derivative of ((sqrt(x)/3+1)^{3/2}) ?
The derivative of ((sqrt(x)/3+1)^{3/2}) is ((sqrt(x)+3)^{1/2})/(4*3^{1/2)x^{1/2}}
What is the first derivative of ((sqrt(x)/3+1)^{3/2}) ?
The first derivative of ((sqrt(x)/3+1)^{3/2}) is ((sqrt(x)+3)^{1/2})/(4*3^{1/2)x^{1/2}}