What is the derivative of 5^{2x}sqrt(x) ?

The derivative of 5^{2x}sqrt(x) is 2ln(5)*25^xsqrt(x)+(25^x)/(2sqrt(x))

What is the first derivative of 5^{2x}sqrt(x) ?

The first derivative of 5^{2x}sqrt(x) is 2ln(5)*25^xsqrt(x)+(25^x)/(2sqrt(x))

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derivative of

5^{2 x} x

2 ln (5) \cdot 2 5^{x} x + \frac{2 5 ^{x}}{2 x}

Solution steps

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

Simplify

5^{2 x} x : 2 5^{x} x

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

Apply the Product Rule:

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

f = 2 5^{x}, g = x

= \frac{d}{d x} (2 5^{x}) x + \frac{d}{d x} (x) 2 5^{x}

\frac{d}{d x} (2 5^{x}) = 2 ln (5) \cdot 2 5^{x}

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

= 2 ln (5) \cdot 2 5^{x} x + \frac{1}{2 x} \cdot 2 5^{x}

\frac{1}{2 x} \cdot 2 5^{x} = \frac{2 5 ^{x}}{2 x}

= 2 ln (5) \cdot 2 5^{x} x + \frac{2 5 ^{x}}{2 x}

\frac{d}{d x} (x^{4} + 4^{x})

x \to + 0 lim (\frac{e ^{- 5 x} - 1}{x})

\frac{\partial}{\partial x} (e^{x y} + x^{2} z)

\int cos^{2} (θ) d θ

\frac{d ^{2}}{d x ^{2}} f (x) = \frac{7}{x + 4}, at x = 0

What is the derivative of 5^{2x}sqrt(x) ?
The derivative of 5^{2x}sqrt(x) is 2ln(5)*25^xsqrt(x)+(25^x)/(2sqrt(x))
What is the first derivative of 5^{2x}sqrt(x) ?
The first derivative of 5^{2x}sqrt(x) is 2ln(5)*25^xsqrt(x)+(25^x)/(2sqrt(x))