What is the derivative of 5^xln(x) ?

The derivative of 5^xln(x) is ln(5)*5^xln(x)+(5^x)/x

What is the first derivative of 5^xln(x) ?

The first derivative of 5^xln(x) is ln(5)*5^xln(x)+(5^x)/x

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

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

Solution steps

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

Apply the Product Rule:

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

f = 5^{x}, g = ln (x)

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

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

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

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

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

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

(2 x y - 3) d x + (x^{2} + 4 y) d y = 0

\int_{0}^{l n (18)} x e^{x} d x

\frac{d}{d x} (e^{i x} + e^{- i x})

\int 6 e^{- 3 x} d x

\int arccot (15 y) d y

What is the derivative of 5^xln(x) ?
The derivative of 5^xln(x) is ln(5)*5^xln(x)+(5^x)/x
What is the first derivative of 5^xln(x) ?
The first derivative of 5^xln(x) is ln(5)*5^xln(x)+(5^x)/x