What is the derivative of y=((sqrt(x))/7+6)^{3/2} ?

The derivative of y=((sqrt(x))/7+6)^{3/2} is (3(sqrt(x)+42)^{1/2})/(28*7^{1/2)x^{1/2}}

What is the first derivative of y=((sqrt(x))/7+6)^{3/2} ?

The first derivative of y=((sqrt(x))/7+6)^{3/2} is (3(sqrt(x)+42)^{1/2})/(28*7^{1/2)x^{1/2}}

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derivative of

y = (\frac{x}{7} + 6)^{\frac{3}{2}}

\frac{3 ( x + 42 ) ^{\frac{1}{2}}}{28 \cdot 7 ^{\frac{1}{2}} x ^{\frac{1}{2}}}

Solution steps

\frac{d}{d x} ((\frac{x}{7} + 6)^{\frac{3}{2}})

Simplify

(\frac{x}{7} + 6)^{\frac{3}{2}} : (\frac{x + 42}{7})^{\frac{3}{2}}

= \frac{d}{d x} ((\frac{x + 42}{7})^{\frac{3}{2}})

Apply the chain rule:

\frac{3 ( \frac{x + 42}{7} ) ^{\frac{1}{2}}}{2} \frac{d}{d x} (\frac{x + 42}{7})

= \frac{3 ( \frac{x + 42}{7} ) ^{\frac{1}{2}}}{2} \frac{d}{d x} (\frac{x + 42}{7})

\frac{d}{d x} (\frac{x + 42}{7}) = \frac{1}{14 x ^{\frac{1}{2}}}

= \frac{3 ( \frac{x + 42}{7} ) ^{\frac{1}{2}}}{2} \cdot \frac{1}{14 x ^{\frac{1}{2}}}

Simplify

\frac{3 ( \frac{x + 42}{7} ) ^{\frac{1}{2}}}{2} \cdot \frac{1}{14 x ^{\frac{1}{2}}} : \frac{3 ( x + 42 ) ^{\frac{1}{2}}}{28 \cdot 7 ^{\frac{1}{2}} x ^{\frac{1}{2}}}

= \frac{3 ( x + 42 ) ^{\frac{1}{2}}}{28 \cdot 7 ^{\frac{1}{2}} x ^{\frac{1}{2}}}

\int \frac{2 e ^{x}}{e ^{2 x} + 2 e ^{x} + 1} d x

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

x y^{^{'}} = y + x e^{\frac{y}{x}}

e^{3 x}, e^{x}, [0, 1]

\int_{- 6}^{8} 10 d x

What is the derivative of y=((sqrt(x))/7+6)^{3/2} ?
The derivative of y=((sqrt(x))/7+6)^{3/2} is (3(sqrt(x)+42)^{1/2})/(28*7^{1/2)x^{1/2}}
What is the first derivative of y=((sqrt(x))/7+6)^{3/2} ?
The first derivative of y=((sqrt(x))/7+6)^{3/2} is (3(sqrt(x)+42)^{1/2})/(28*7^{1/2)x^{1/2}}