What is the derivative of x^3(x^2+4+1/x) ?

The derivative of x^3(x^2+4+1/x) is 5x^4+12x^2+2x

What is the first derivative of x^3(x^2+4+1/x) ?

The first derivative of x^3(x^2+4+1/x) is 5x^4+12x^2+2x

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

5 x^{4} + 12 x^{2} + 2 x

Solution steps

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

Apply the Product Rule:

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

f = x^{3}, g = x^{2} + 4 + \frac{1}{x}

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

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

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

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

Simplify

3 x^{2} (x^{2} + 4 + \frac{1}{x}) + (2 x - \frac{1}{x ^{2}}) x^{3} : 5 x^{4} + 12 x^{2} + 2 x

= 5 x^{4} + 12 x^{2} + 2 x

\frac{d}{d x} (x^{2} + 2 y^{2} + z^{2} - 6 x + 3 y - 2 z + 5)

y^{^{''}} - 6 y^{^{'}} + 0 y = 0

\int \frac{5}{e ^{x} + 2} d x

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

\frac{d y}{d x} + 3 x y^{3} = 0

What is the derivative of x^3(x^2+4+1/x) ?
The derivative of x^3(x^2+4+1/x) is 5x^4+12x^2+2x
What is the first derivative of x^3(x^2+4+1/x) ?
The first derivative of x^3(x^2+4+1/x) is 5x^4+12x^2+2x