What is the derivative of ((x^5+1)/x)(x^5+1) ?

The derivative of ((x^5+1)/x)(x^5+1) is (9x^{10}+8x^5-1)/(x^2)

What is the first derivative of ((x^5+1)/x)(x^5+1) ?

The first derivative of ((x^5+1)/x)(x^5+1) is (9x^{10}+8x^5-1)/(x^2)

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derivative of

(\frac{x ^{5} + 1}{x}) (x^{5} + 1)

\frac{9 x ^{10} + 8 x ^{5} - 1}{x ^{2}}

Solution steps

\frac{d}{d x} (\frac{x ^{5} + 1}{x} (x^{5} + 1))

Apply the Product Rule:

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

f = \frac{x ^{5} + 1}{x}, g = x^{5} + 1

= \frac{d}{d x} (\frac{x ^{5} + 1}{x}) (x^{5} + 1) + \frac{d}{d x} (x^{5} + 1) \frac{x ^{5} + 1}{x}

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

\frac{d}{d x} (x^{5} + 1) = 5 x^{4}

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

Simplify

\frac{4 x ^{5} - 1}{x ^{2}} (x^{5} + 1) + 5 x^{4} \frac{x ^{5} + 1}{x} : \frac{9 x ^{10} + 8 x ^{5} - 1}{x ^{2}}

= \frac{9 x ^{10} + 8 x ^{5} - 1}{x ^{2}}

4 x - 5

(e^{x + 1})^{\frac{1}{2}}

\frac{d}{d t} (100 - 10 t + 6 t^{2})

y = x^{7} + 3 x^{5} + 1

4 x^{\frac{1}{3}}

What is the derivative of ((x^5+1)/x)(x^5+1) ?
The derivative of ((x^5+1)/x)(x^5+1) is (9x^{10}+8x^5-1)/(x^2)
What is the first derivative of ((x^5+1)/x)(x^5+1) ?
The first derivative of ((x^5+1)/x)(x^5+1) is (9x^{10}+8x^5-1)/(x^2)