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Popular >

derivative of x^5e^{3x}

Solution

\frac{d}{d x} (x^{5} e^{3 x})

Solution

5 x^{4} e^{3 x} + e^{3 x} \cdot 3 x^{5}

Solution steps

\frac{d}{d x} (x^{5} e^{3 x})

Apply the Product Rule:

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

f = x^{5}, g = e^{3 x}

= \frac{d}{d x} (x^{5}) e^{3 x} + \frac{d}{d x} (e^{3 x}) x^{5}

\frac{d}{d x} (x^{5}) = 5 x^{4}

\frac{d}{d x} (e^{3 x}) = e^{3 x} \cdot 3

= 5 x^{4} e^{3 x} + e^{3 x} \cdot 3 x^{5}

Popular Examples

integral of 9x^5e^{x^6}

\int 9 x^{5} e^{x^{6}} d x

implicit (dy)/(dx),x^2-xy+y^2=19 implicit derivative

\frac{d y}{d x}, x^{2} - x y + y^{2} = 19

(\partial)/(\partial x)((5s-3t)/(4s+5t))

\frac{\partial}{\partial x} (\frac{5 s - 3 t}{4 s + 5 t})

limit as x approaches 0-of (7e^x)/(x^5)

x \to 0 - lim (\frac{7 e ^{x}}{x ^{5}})

(dy)/(dx)=(xy+3x-y-3)/(xy-2x+4y-8)

\frac{d y}{d x} = \frac{x y + 3 x - y - 3}{x y - 2 x + 4 y - 8}

Frequently Asked Questions (FAQ)

What is the derivative of x^5e^{3x} ?
The derivative of x^5e^{3x} is 5x^4e^{3x}+e^{3x}*3x^5
What is the first derivative of x^5e^{3x} ?
The first derivative of x^5e^{3x} is 5x^4e^{3x}+e^{3x}*3x^5