What is the derivative of (x^2-8x+8e^{(9x)/8}) ?

The derivative of (x^2-8x+8e^{(9x)/8}) is (9e^{(9x)/8}x^2)/(8)-7e^{(9x)/8}x+e^{(9x)/8}

What is the first derivative of (x^2-8x+8e^{(9x)/8}) ?

The first derivative of (x^2-8x+8e^{(9x)/8}) is (9e^{(9x)/8}x^2)/(8)-7e^{(9x)/8}x+e^{(9x)/8}

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\frac{d}{d x} ((x^{2} - 8 x + 8) e^{\frac{9 x}{8}})

\frac{9 e ^{\frac{9 x}{8}} x ^{2}}{8} - 7 e^{\frac{9 x}{8}} x + e^{\frac{9 x}{8}}

Solution steps

\frac{d}{d x} ((x^{2} - 8 x + 8) e^{\frac{9 x}{8}})

Apply the Product Rule:

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

f = x^{2} - 8 x + 8, g = e^{\frac{9 x}{8}}

= \frac{d}{d x} (x^{2} - 8 x + 8) e^{\frac{9 x}{8}} + \frac{d}{d x} (e^{\frac{9 x}{8}}) (x^{2} - 8 x + 8)

\frac{d}{d x} (x^{2} - 8 x + 8) = 2 x - 8

\frac{d}{d x} (e^{\frac{9 x}{8}}) = e^{\frac{9 x}{8}} \frac{9}{8}

= (2 x - 8) e^{\frac{9 x}{8}} + e^{\frac{9 x}{8}} \frac{9}{8} (x^{2} - 8 x + 8)

Simplify

(2 x - 8) e^{\frac{9 x}{8}} + e^{\frac{9 x}{8}} \frac{9}{8} (x^{2} - 8 x + 8) : \frac{9 e ^{\frac{9 x}{8}} x ^{2}}{8} - 7 e^{\frac{9 x}{8}} x + e^{\frac{9 x}{8}}

= \frac{9 e ^{\frac{9 x}{8}} x ^{2}}{8} - 7 e^{\frac{9 x}{8}} x + e^{\frac{9 x}{8}}

x^{x}

(3 - x^{2})^{2}, x^{4}

(2 x + 3)^{1.4}

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

(2 x^{2} + 1) (x - 3)^{2}

What is the derivative of (x^2-8x+8e^{(9x)/8}) ?
The derivative of (x^2-8x+8e^{(9x)/8}) is (9e^{(9x)/8}x^2)/(8)-7e^{(9x)/8}x+e^{(9x)/8}
What is the first derivative of (x^2-8x+8e^{(9x)/8}) ?
The first derivative of (x^2-8x+8e^{(9x)/8}) is (9e^{(9x)/8}x^2)/(8)-7e^{(9x)/8}x+e^{(9x)/8}