What is the derivative of f(x)=(x^5+x^9)/x ?

The derivative of f(x)=(x^5+x^9)/x is 8x^7+4x^3

What is the first derivative of f(x)=(x^5+x^9)/x ?

The first derivative of f(x)=(x^5+x^9)/x is 8x^7+4x^3

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derivative of

f (x) = \frac{x ^{5} + x ^{9}}{x}

8 x^{7} + 4 x^{3}

Solution steps

\frac{d}{d x} (\frac{x ^{5} + x ^{9}}{x})

Simplify

\frac{x ^{5} + x ^{9}}{x} : x^{4} (x^{4} + 1)

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

Apply the Product Rule:

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

f = x^{4}, g = x^{4} + 1

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

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

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

= 4 x^{3} (x^{4} + 1) + 4 x^{3} x^{4}

Simplify

4 x^{3} (x^{4} + 1) + 4 x^{3} x^{4} : 8 x^{7} + 4 x^{3}

= 8 x^{7} + 4 x^{3}

y = 8 e^{- x} + e^{3 x}

x \to 0 lim (1 - \frac{cos ( x )}{x})

\frac{5 + x - 5}{x}

d y - (y - 8)^{2} d x = 0

\frac{\partial}{\partial x} (x^{2} y^{3} + (x - y)^{2})

What is the derivative of f(x)=(x^5+x^9)/x ?
The derivative of f(x)=(x^5+x^9)/x is 8x^7+4x^3
What is the first derivative of f(x)=(x^5+x^9)/x ?
The first derivative of f(x)=(x^5+x^9)/x is 8x^7+4x^3