What is the derivative of 30e^xsqrt(x) ?

The derivative of 30e^xsqrt(x) is 30(e^xsqrt(x)+(e^x)/(2sqrt(x)))

What is the first derivative of 30e^xsqrt(x) ?

The first derivative of 30e^xsqrt(x) is 30(e^xsqrt(x)+(e^x)/(2sqrt(x)))

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derivative of

30 e^{x} x

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

Solution steps

\frac{d}{d x} (30 e^{x} x)

Take the constant out:

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

= 30 \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

= 30 (\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}

= 30 (e^{x} x + \frac{1}{2 x} e^{x})

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

= 30 (e^{x} x + \frac{e ^{x}}{2 x})

\int_{0}^{1} (u + 2) (u - 3) d u

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

x \to 0 lim (\frac{1}{2 ^{x}})

sin (tan (2 x))

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

What is the derivative of 30e^xsqrt(x) ?
The derivative of 30e^xsqrt(x) is 30(e^xsqrt(x)+(e^x)/(2sqrt(x)))
What is the first derivative of 30e^xsqrt(x) ?
The first derivative of 30e^xsqrt(x) is 30(e^xsqrt(x)+(e^x)/(2sqrt(x)))