What is the derivative of f(x)=7x^6e^x+e^xx^7 ?

The derivative of f(x)=7x^6e^x+e^xx^7 is e^xx^7+14e^xx^6+42e^xx^5

What is the first derivative of f(x)=7x^6e^x+e^xx^7 ?

The first derivative of f(x)=7x^6e^x+e^xx^7 is e^xx^7+14e^xx^6+42e^xx^5

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derivative of

f (x) = 7 x^{6} e^{x} + e^{x} x^{7}

e^{x} x^{7} + 14 e^{x} x^{6} + 42 e^{x} x^{5}

Solution steps

\frac{d}{d x} (7 x^{6} e^{x} + e^{x} x^{7})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (7 x^{6} e^{x}) + \frac{d}{d x} (e^{x} x^{7})

\frac{d}{d x} (7 x^{6} e^{x}) = 7 (6 x^{5} e^{x} + e^{x} x^{6})

\frac{d}{d x} (e^{x} x^{7}) = e^{x} x^{7} + 7 x^{6} e^{x}

= 7 (6 x^{5} e^{x} + e^{x} x^{6}) + e^{x} x^{7} + 7 x^{6} e^{x}

Simplify

7 (6 x^{5} e^{x} + e^{x} x^{6}) + e^{x} x^{7} + 7 x^{6} e^{x} : e^{x} x^{7} + 14 e^{x} x^{6} + 42 e^{x} x^{5}

= e^{x} x^{7} + 14 e^{x} x^{6} + 42 e^{x} x^{5}

\frac{3}{s ( 6 s ^{2} + 5 s + 1 )}

\frac{\partial}{\partial y} (cos (x yz))

y^{^{''}} + 45 y^{^{'}} + 20 y = 0, y (0) = 1, y^{^{'}} (0) = 0

n = 1 \sum \infty n e^{3 n}

x \to 0 + lim (\frac{6}{x ^{2}})

What is the derivative of f(x)=7x^6e^x+e^xx^7 ?
The derivative of f(x)=7x^6e^x+e^xx^7 is e^xx^7+14e^xx^6+42e^xx^5
What is the first derivative of f(x)=7x^6e^x+e^xx^7 ?
The first derivative of f(x)=7x^6e^x+e^xx^7 is e^xx^7+14e^xx^6+42e^xx^5