What is the derivative of e^x(x^2+1)(x+4) ?

The derivative of e^x(x^2+1)(x+4) is e^xx^3+7e^xx^2+9e^xx+5e^x

What is the first derivative of e^x(x^2+1)(x+4) ?

The first derivative of e^x(x^2+1)(x+4) is e^xx^3+7e^xx^2+9e^xx+5e^x

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derivative of

e^{x} (x^{2} + 1) (x + 4)

e^{x} x^{3} + 7 e^{x} x^{2} + 9 e^{x} x + 5 e^{x}

Solution steps

\frac{d}{d x} (e^{x} (x^{2} + 1) (x + 4))

Apply the Product Rule:

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

f = e^{x}, g = (x^{2} + 1) (x + 4)

= \frac{d}{d x} (e^{x}) (x^{2} + 1) (x + 4) + \frac{d}{d x} ((x^{2} + 1) (x + 4)) e^{x}

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

\frac{d}{d x} ((x^{2} + 1) (x + 4)) = 3 x^{2} + 8 x + 1

= e^{x} (x^{2} + 1) (x + 4) + (3 x^{2} + 8 x + 1) e^{x}

Simplify

e^{x} (x^{2} + 1) (x + 4) + (3 x^{2} + 8 x + 1) e^{x} : e^{x} x^{3} + 7 e^{x} x^{2} + 9 e^{x} x + 5 e^{x}

= e^{x} x^{3} + 7 e^{x} x^{2} + 9 e^{x} x + 5 e^{x}

x^{\frac{1}{3}}, 1

y = - x, y = - x^{2} + e x

\frac{csc ( 3 x )}{x ^{3}}

f (x) = x^{2} + 4 x - 4

\int 13 x^{12} d x

What is the derivative of e^x(x^2+1)(x+4) ?
The derivative of e^x(x^2+1)(x+4) is e^xx^3+7e^xx^2+9e^xx+5e^x
What is the first derivative of e^x(x^2+1)(x+4) ?
The first derivative of e^x(x^2+1)(x+4) is e^xx^3+7e^xx^2+9e^xx+5e^x