What is the derivative of e^{4x}ln(y) ?

The derivative of e^{4x}ln(y) is 4e^{4x}ln(y)+(e^{4x}(dy)/(dx))/y

What is the first derivative of e^{4x}ln(y) ?

The first derivative of e^{4x}ln(y) is 4e^{4x}ln(y)+(e^{4x}(dy)/(dx))/y

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\frac{d}{d x} (e^{4 x} ln (y))

4 e^{4 x} ln (y) + \frac{e ^{4 x} \frac{d y}{d x}}{y}

Solution steps

\frac{d}{d x} (e^{4 x} ln (y))

Apply the Product Rule:

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

f = e^{4 x}, g = ln (y)

= \frac{d}{d x} (e^{4 x}) ln (y) + \frac{d}{d x} (ln (y)) e^{4 x}

\frac{d}{d x} (e^{4 x}) = e^{4 x} \cdot 4

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

= e^{4 x} \cdot 4 ln (y) + \frac{\frac{d y}{d x}}{y} e^{4 x}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= 4 e^{4 x} ln (y) + \frac{e ^{4 x} \frac{d y}{d x}}{y}

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

\int csc^{2} (8 θ) cot (8 θ) d θ

f (θ) = cos (θ^{2})

\int_{0}^{1} x^{2} sin (nπ x) d x

What is the derivative of e^{4x}ln(y) ?
The derivative of e^{4x}ln(y) is 4e^{4x}ln(y)+(e^{4x}(dy)/(dx))/y
What is the first derivative of e^{4x}ln(y) ?
The first derivative of e^{4x}ln(y) is 4e^{4x}ln(y)+(e^{4x}(dy)/(dx))/y