What is the derivative of f(x)=x^6*e^x ?

The derivative of f(x)=x^6*e^x is 6x^5e^x+e^xx^6

What is the first derivative of f(x)=x^6*e^x ?

The first derivative of f(x)=x^6*e^x is 6x^5e^x+e^xx^6

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derivative of

f (x) = x^{6} \cdot e^{x}

6 x^{5} e^{x} + e^{x} x^{6}

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d}{d x} (x^{6}) = 6 x^{5}

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

= 6 x^{5} e^{x} + e^{x} x^{6}

f (x) = \frac{3}{4 x}

(4 x - 5)^{3} (1 - x^{5})^{2}

y^{^{'}} = (x + y)^{2}, y (0) = 1

sin (x)

\frac{\partial}{\partial x} (2 + y ln (4 + x (y)^{2}))

What is the derivative of f(x)=x^6*e^x ?
The derivative of f(x)=x^6*e^x is 6x^5e^x+e^xx^6
What is the first derivative of f(x)=x^6*e^x ?
The first derivative of f(x)=x^6*e^x is 6x^5e^x+e^xx^6