What is the derivative of (2-x+3x^2(x^3+5e^x)) ?

The derivative of (2-x+3x^2(x^3+5e^x)) is 15x^4-4x^3+6x^2+15e^xx^2+25e^xx+5e^x

What is the first derivative of (2-x+3x^2(x^3+5e^x)) ?

The first derivative of (2-x+3x^2(x^3+5e^x)) is 15x^4-4x^3+6x^2+15e^xx^2+25e^xx+5e^x

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\frac{d}{d x} ((2 - x + 3 x^{2}) (x^{3} + 5 e^{x}))

15 x^{4} - 4 x^{3} + 6 x^{2} + 15 e^{x} x^{2} + 25 e^{x} x + 5 e^{x}

Solution steps

\frac{d}{d x} ((2 - x + 3 x^{2}) (x^{3} + 5 e^{x}))

Apply the Product Rule:

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

f = 2 - x + 3 x^{2}, g = x^{3} + 5 e^{x}

= \frac{d}{d x} (2 - x + 3 x^{2}) (x^{3} + 5 e^{x}) + \frac{d}{d x} (x^{3} + 5 e^{x}) (2 - x + 3 x^{2})

\frac{d}{d x} (2 - x + 3 x^{2}) = 6 x - 1

\frac{d}{d x} (x^{3} + 5 e^{x}) = 3 x^{2} + 5 e^{x}

= (6 x - 1) (x^{3} + 5 e^{x}) + (3 x^{2} + 5 e^{x}) (2 - x + 3 x^{2})

Simplify

(6 x - 1) (x^{3} + 5 e^{x}) + (3 x^{2} + 5 e^{x}) (2 - x + 3 x^{2}) : 15 x^{4} - 4 x^{3} + 6 x^{2} + 15 e^{x} x^{2} + 25 e^{x} x + 5 e^{x}

= 15 x^{4} - 4 x^{3} + 6 x^{2} + 15 e^{x} x^{2} + 25 e^{x} x + 5 e^{x}

\int \frac{1}{2 - sin ^{2} ( x )} d x

(0) (4.2)

\int \frac{- 5}{( x + 2 ) ^{2}} d x

\int - x^{2} + 2 d x

t \frac{d x}{d t} + 2 x = 3 t

What is the derivative of (2-x+3x^2(x^3+5e^x)) ?
The derivative of (2-x+3x^2(x^3+5e^x)) is 15x^4-4x^3+6x^2+15e^xx^2+25e^xx+5e^x
What is the first derivative of (2-x+3x^2(x^3+5e^x)) ?
The first derivative of (2-x+3x^2(x^3+5e^x)) is 15x^4-4x^3+6x^2+15e^xx^2+25e^xx+5e^x