What is the derivative of x^{8e^{5x}} ?

The derivative of x^{8e^{5x}} is 8x^{8e^{5x}}(5e^{5x}ln(x)+(e^{5x})/x)

What is the first derivative of x^{8e^{5x}} ?

The first derivative of x^{8e^{5x}} is 8x^{8e^{5x}}(5e^{5x}ln(x)+(e^{5x})/x)

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\frac{d}{d x} (x^{8 e^{5 x}})

8 x^{8 e^{5 x}} (5 e^{5 x} ln (x) + \frac{e ^{5 x}}{x})

Solution steps

\frac{d}{d x} (x^{8 e^{5 x}})

Apply exponent rule:

a^{b} = e^{b l n (a)}

x^{8 e^{5 x}} = e^{8 e^{5 x} l n (x)}

= \frac{d}{d x} (e^{8 e^{5 x} l n (x)})

Apply the chain rule:

e^{8 e^{5 x} l n (x)} \frac{d}{d x} (8 e^{5 x} ln (x))

= e^{8 e^{5 x} l n (x)} \frac{d}{d x} (8 e^{5 x} ln (x))

\frac{d}{d x} (8 e^{5 x} ln (x)) = 8 (5 e^{5 x} ln (x) + \frac{e ^{5 x}}{x})

= e^{8 e^{5 x} l n (x)} \cdot 8 (5 e^{5 x} ln (x) + \frac{e ^{5 x}}{x})

e^{8 e^{5 x} l n (x)} = x^{8 e^{5 x}}

= 8 x^{8 e^{5 x}} (5 e^{5 x} ln (x) + \frac{e ^{5 x}}{x})

\frac{d}{d x} (12 x (x^{2} + 10)^{5})

\int 2 sin^{2} (x) cos (x) d x

\int 2 x x + 3 d x

\int x^{e} + e^{x} d x

\frac{\partial}{\partial x} (cos (y^{2}))

What is the derivative of x^{8e^{5x}} ?
The derivative of x^{8e^{5x}} is 8x^{8e^{5x}}(5e^{5x}ln(x)+(e^{5x})/x)
What is the first derivative of x^{8e^{5x}} ?
The first derivative of x^{8e^{5x}} is 8x^{8e^{5x}}(5e^{5x}ln(x)+(e^{5x})/x)