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

The derivative of (2)(e^{3xsqrt(x)}) is 9e^{3x^{3/2}}sqrt(x)

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

The first derivative of (2)(e^{3xsqrt(x)}) is 9e^{3x^{3/2}}sqrt(x)

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derivative of

(2) (e^{3 x x})

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

Solution steps

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

Simplify

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

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

Take the constant out:

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

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

Apply the chain rule:

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

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

\frac{d}{d x} (3 x^{\frac{3}{2}}) = \frac{9 x}{2}

= 2 e^{3 x^{\frac{3}{2}}} \frac{9 x}{2}

Simplify

2 e^{3 x^{\frac{3}{2}}} \frac{9 x}{2} : 9 e^{3 x^{\frac{3}{2}}} x

= 9 e^{3 x^{\frac{3}{2}}} x

\int (x + 1) e^{8 x^{2} + 16 x} d x

\frac{\partial}{\partial x} (\frac{1}{2 x + y})

x \to 5 lim (\frac{x - 5}{x ^{2} - 5})

\int \frac{tan ^{4} ( x )}{cos ^{2} ( x )} d x

\frac{d y}{d x} = y e^{x}, y (0) = 2 e

What is the derivative of (2)(e^{3xsqrt(x)}) ?
The derivative of (2)(e^{3xsqrt(x)}) is 9e^{3x^{3/2}}sqrt(x)
What is the first derivative of (2)(e^{3xsqrt(x)}) ?
The first derivative of (2)(e^{3xsqrt(x)}) is 9e^{3x^{3/2}}sqrt(x)