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Popular >

derivative of y=(x^4-6x)e^x

Solution

derivative of

y = (x^{4} - 6 x) e^{x}

Solution

(4 x^{3} - 6) e^{x} + e^{x} (x^{4} - 6 x)

Solution steps

\frac{d}{d x} ((x^{4} - 6 x) e^{x})

Apply the Product Rule:

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

f = x^{4} - 6 x, g = e^{x}

= \frac{d}{d x} (x^{4} - 6 x) e^{x} + \frac{d}{d x} (e^{x}) (x^{4} - 6 x)

\frac{d}{d x} (x^{4} - 6 x) = 4 x^{3} - 6

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

= (4 x^{3} - 6) e^{x} + e^{x} (x^{4} - 6 x)

Popular Examples

(\partial)/(\partial x)((2x)/(x^2+y^2+16))

\frac{\partial}{\partial x} (\frac{2 x}{x ^{2} + y ^{2} + 16})

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\frac{d}{d x} (\frac{cos ( 2 x )}{x})

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\frac{\partial}{\partial x} (ln (\frac{( x + y )}{x - y}))

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\frac{d}{d x} ((4 x + 1)^{2})

Frequently Asked Questions (FAQ)

What is the derivative of y=(x^4-6x)e^x ?
The derivative of y=(x^4-6x)e^x is (4x^3-6)e^x+e^x(x^4-6x)
What is the first derivative of y=(x^4-6x)e^x ?
The first derivative of y=(x^4-6x)e^x is (4x^3-6)e^x+e^x(x^4-6x)