What is the derivative of y=(x^2-7x+7)e^{(9x)/7} ?

The derivative of y=(x^2-7x+7)e^{(9x)/7} is (9e^{(9x)/7}x^2)/(7)-7e^{(9x)/7}x+2e^{(9x)/7}

What is the first derivative of y=(x^2-7x+7)e^{(9x)/7} ?

The first derivative of y=(x^2-7x+7)e^{(9x)/7} is (9e^{(9x)/7}x^2)/(7)-7e^{(9x)/7}x+2e^{(9x)/7}

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derivative of

y = (x^{2} - 7 x + 7) e^{\frac{9 x}{7}}

\frac{9 e ^{\frac{9 x}{7}} x ^{2}}{7} - 7 e^{\frac{9 x}{7}} x + 2 e^{\frac{9 x}{7}}

Solution steps

\frac{d}{d x} ((x^{2} - 7 x + 7) e^{\frac{9 x}{7}})

Apply the Product Rule:

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

f = x^{2} - 7 x + 7, g = e^{\frac{9 x}{7}}

= \frac{d}{d x} (x^{2} - 7 x + 7) e^{\frac{9 x}{7}} + \frac{d}{d x} (e^{\frac{9 x}{7}}) (x^{2} - 7 x + 7)

\frac{d}{d x} (x^{2} - 7 x + 7) = 2 x - 7

\frac{d}{d x} (e^{\frac{9 x}{7}}) = e^{\frac{9 x}{7}} \frac{9}{7}

= (2 x - 7) e^{\frac{9 x}{7}} + e^{\frac{9 x}{7}} \frac{9}{7} (x^{2} - 7 x + 7)

Simplify

(2 x - 7) e^{\frac{9 x}{7}} + e^{\frac{9 x}{7}} \frac{9}{7} (x^{2} - 7 x + 7) : \frac{9 e ^{\frac{9 x}{7}} x ^{2}}{7} - 7 e^{\frac{9 x}{7}} x + 2 e^{\frac{9 x}{7}}

= \frac{9 e ^{\frac{9 x}{7}} x ^{2}}{7} - 7 e^{\frac{9 x}{7}} x + 2 e^{\frac{9 x}{7}}

\int_{0}^{\infty} cos (x) d x

\int (6 x^{2} + 8 x + 3) d x

y^{^{'}} = 8 x^{3} e^{- 2 y}

\frac{d}{d x} (- e^{- \frac{x ^{2}}{2}} x)

\frac{( 2 + s )}{s ^{2} + 2 s + 2}

What is the derivative of y=(x^2-7x+7)e^{(9x)/7} ?
The derivative of y=(x^2-7x+7)e^{(9x)/7} is (9e^{(9x)/7}x^2)/(7)-7e^{(9x)/7}x+2e^{(9x)/7}
What is the first derivative of y=(x^2-7x+7)e^{(9x)/7} ?
The first derivative of y=(x^2-7x+7)e^{(9x)/7} is (9e^{(9x)/7}x^2)/(7)-7e^{(9x)/7}x+2e^{(9x)/7}