What is the derivative of f(x)=2e^x*(x^2+3x-9)^2 ?

The derivative of f(x)=2e^x*(x^2+3x-9)^2 is 2(e^xx^4+10e^xx^3+9e^xx^2-72e^xx+27e^x)

What is the first derivative of f(x)=2e^x*(x^2+3x-9)^2 ?

The first derivative of f(x)=2e^x*(x^2+3x-9)^2 is 2(e^xx^4+10e^xx^3+9e^xx^2-72e^xx+27e^x)

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derivative of

f (x) = 2 e^{x} \cdot (x^{2} + 3 x - 9)^{2}

2 (e^{x} x^{4} + 10 e^{x} x^{3} + 9 e^{x} x^{2} - 72 e^{x} x + 27 e^{x})

Solution steps

\frac{d}{d x} (2 e^{x} (x^{2} + 3 x - 9)^{2})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 2 \frac{d}{d x} (e^{x} (x^{2} + 3 x - 9)^{2})

Apply the Product Rule:

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

f = e^{x}, g = (x^{2} + 3 x - 9)^{2}

= 2 (\frac{d}{d x} (e^{x}) (x^{2} + 3 x - 9)^{2} + \frac{d}{d x} ((x^{2} + 3 x - 9)^{2}) e^{x})

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

\frac{d}{d x} ((x^{2} + 3 x - 9)^{2}) = 2 (x^{2} + 3 x - 9) (2 x + 3)

= 2 (e^{x} (x^{2} + 3 x - 9)^{2} + 2 (x^{2} + 3 x - 9) (2 x + 3) e^{x})

Expand

e^{x} (x^{2} + 3 x - 9)^{2} + 2 (x^{2} + 3 x - 9) (2 x + 3) e^{x} : e^{x} x^{4} + 10 e^{x} x^{3} + 9 e^{x} x^{2} - 72 e^{x} x + 27 e^{x}

= 2 (e^{x} x^{4} + 10 e^{x} x^{3} + 9 e^{x} x^{2} - 72 e^{x} x + 27 e^{x})

\frac{d}{d θ} (\frac{cos ( θ )}{sin ( θ )})

x \to + 0 lim (x - 3)

2^{4 x}

\int 2 x 4 x^{2} + 1 d x

n = 0 \sum \infty \frac{2}{n ^{2} + 4 n + 3}

What is the derivative of f(x)=2e^x*(x^2+3x-9)^2 ?
The derivative of f(x)=2e^x*(x^2+3x-9)^2 is 2(e^xx^4+10e^xx^3+9e^xx^2-72e^xx+27e^x)
What is the first derivative of f(x)=2e^x*(x^2+3x-9)^2 ?
The first derivative of f(x)=2e^x*(x^2+3x-9)^2 is 2(e^xx^4+10e^xx^3+9e^xx^2-72e^xx+27e^x)