What is the derivative of f(x)=(4x)/(x^3+5) ?

The derivative of f(x)=(4x)/(x^3+5) is (4(-2x^3+5))/((x^3+5)^2)

What is the first derivative of f(x)=(4x)/(x^3+5) ?

The first derivative of f(x)=(4x)/(x^3+5) is (4(-2x^3+5))/((x^3+5)^2)

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derivative of

f (x) = \frac{4 x}{x ^{3} + 5}

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

Solution steps

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

Take the constant out:

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

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

\frac{d x}{d x} = 1

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

= 4 \cdot \frac{1 \cdot ( x ^{3} + 5 ) - 3 x ^{2} x}{( x ^{3} + 5 ) ^{2}}

Simplify

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

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

\int \frac{80}{64 - x ^{2}} d x

\frac{\partial}{\partial x} (f (x, b, y) (a x + b y))

5 x, \frac{1}{7} x, 50 - x^{2}

(x^{2} + 1) y^{^{'}} + 7 x (y - 1) = 0, y (0) = 4

x \to \infty lim (cos (0))

What is the derivative of f(x)=(4x)/(x^3+5) ?
The derivative of f(x)=(4x)/(x^3+5) is (4(-2x^3+5))/((x^3+5)^2)
What is the first derivative of f(x)=(4x)/(x^3+5) ?
The first derivative of f(x)=(4x)/(x^3+5) is (4(-2x^3+5))/((x^3+5)^2)