What is the derivative of (4x^5-2x(3x+e^x)) ?

The derivative of (4x^5-2x(3x+e^x)) is 72x^5+4e^xx^5+20e^xx^4-12x-2e^xx-2e^x

What is the first derivative of (4x^5-2x(3x+e^x)) ?

The first derivative of (4x^5-2x(3x+e^x)) is 72x^5+4e^xx^5+20e^xx^4-12x-2e^xx-2e^x

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\frac{d}{d x} ((4 x^{5} - 2 x) (3 x + e^{x}))

72 x^{5} + 4 e^{x} x^{5} + 20 e^{x} x^{4} - 12 x - 2 e^{x} x - 2 e^{x}

Solution steps

\frac{d}{d x} ((4 x^{5} - 2 x) (3 x + e^{x}))

Apply the Product Rule:

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

f = 4 x^{5} - 2 x, g = 3 x + e^{x}

= \frac{d}{d x} (4 x^{5} - 2 x) (3 x + e^{x}) + \frac{d}{d x} (3 x + e^{x}) (4 x^{5} - 2 x)

\frac{d}{d x} (4 x^{5} - 2 x) = 20 x^{4} - 2

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

= (20 x^{4} - 2) (3 x + e^{x}) + (3 + e^{x}) (4 x^{5} - 2 x)

Simplify

(20 x^{4} - 2) (3 x + e^{x}) + (3 + e^{x}) (4 x^{5} - 2 x) : 72 x^{5} + 4 e^{x} x^{5} + 20 e^{x} x^{4} - 12 x - 2 e^{x} x - 2 e^{x}

= 72 x^{5} + 4 e^{x} x^{5} + 20 e^{x} x^{4} - 12 x - 2 e^{x} x - 2 e^{x}

\frac{7}{t}

x \to \infty lim (2 x^{3} - 5 x - 4 x^{3})

(x - 2)^{\frac{1}{3}}

\int cot^{3} (6 x) d x

\int_{0}^{1} \frac{2}{2 x ^{2} + 3 x + 1} d x

What is the derivative of (4x^5-2x(3x+e^x)) ?
The derivative of (4x^5-2x(3x+e^x)) is 72x^5+4e^xx^5+20e^xx^4-12x-2e^xx-2e^x
What is the first derivative of (4x^5-2x(3x+e^x)) ?
The first derivative of (4x^5-2x(3x+e^x)) is 72x^5+4e^xx^5+20e^xx^4-12x-2e^xx-2e^x