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Popular >

derivative of 9e^xsqrt(x)

Solution

derivative of

9 e^{x} x

Solution

9 (e^{x} x + \frac{e ^{x}}{2 x})

Solution steps

\frac{d}{d x} (9 e^{x} x)

Take the constant out:

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

= 9 \frac{d}{d x} (e^{x} x)

Apply the Product Rule:

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

f = e^{x}, g = x

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

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

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

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

\frac{1}{2 x} e^{x} = \frac{e ^{x}}{2 x}

= 9 (e^{x} x + \frac{e ^{x}}{2 x})

Popular Examples

(d^{10})/(dx^{10)}(sin(x))

\frac{d ^{10}}{d x ^{10}} (sin (x))

derivative of (x-1^2)

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

derivative of a+x

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

tangent of f(x)=sqrt(x)tangent of

f (x) = x

(\partial)/(\partial x)((4x+3t)/(x-2t))

\frac{\partial}{\partial x} (\frac{4 x + 3 t}{x - 2 t})

Frequently Asked Questions (FAQ)

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