What is the derivative of (e^{3x^2})/(5x) ?

The derivative of (e^{3x^2})/(5x) is (6e^{3x^2}x^2-e^{3x^2})/(5x^2)

What is the first derivative of (e^{3x^2})/(5x) ?

The first derivative of (e^{3x^2})/(5x) is (6e^{3x^2}x^2-e^{3x^2})/(5x^2)

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derivative of

\frac{e ^{3 x^{2}}}{5 x}

\frac{6 e ^{3 x^{2}} x ^{2} - e ^{3 x^{2}}}{5 x ^{2}}

Solution steps

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

Take the constant out:

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

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

\frac{d}{d x} (e^{3 x^{2}}) = e^{3 x^{2}} \cdot 6 x

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

= \frac{1}{5} \cdot \frac{e ^{3 x^{2}} \cdot 6 xx - 1 \cdot e ^{3 x^{2}}}{x ^{2}}

Simplify

\frac{1}{5} \cdot \frac{e ^{3 x^{2}} \cdot 6 xx - 1 \cdot e ^{3 x^{2}}}{x ^{2}} : \frac{6 e ^{3 x^{2}} x ^{2} - e ^{3 x^{2}}}{5 x ^{2}}

= \frac{6 e ^{3 x^{2}} x ^{2} - e ^{3 x^{2}}}{5 x ^{2}}

s l o p e (19.3) (20.3)

\frac{d}{d x} (e^{s i n (x)})

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

\frac{d}{d x} ((2 x^{3} - 12 x)^{\frac{4}{3}})

64 y^{^{''}} + 80 y^{^{'}} + 25 y = 0, y (0) = a, y^{^{'}} (0) = - 5

What is the derivative of (e^{3x^2})/(5x) ?
The derivative of (e^{3x^2})/(5x) is (6e^{3x^2}x^2-e^{3x^2})/(5x^2)
What is the first derivative of (e^{3x^2})/(5x) ?
The first derivative of (e^{3x^2})/(5x) is (6e^{3x^2}x^2-e^{3x^2})/(5x^2)