What is the derivative of f(x)=sqrt(5x)(1+x^2) ?

The derivative of f(x)=sqrt(5x)(1+x^2) is (sqrt(5)+5sqrt(5)x^2)/(2sqrt(x))

What is the first derivative of f(x)=sqrt(5x)(1+x^2) ?

The first derivative of f(x)=sqrt(5x)(1+x^2) is (sqrt(5)+5sqrt(5)x^2)/(2sqrt(x))

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derivative of

f (x) = 5 x (1 + x^{2})

\frac{5 + 5 5 x ^{2}}{2 x}

Solution steps

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

Apply the Product Rule:

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

f = 5 x, g = 1 + x^{2}

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

\frac{d}{d x} (5 x) = \frac{5}{2 x}

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

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

Simplify

\frac{5}{2 x} (1 + x^{2}) + 2 x 5 x : \frac{5 + 5 5 x ^{2}}{2 x}

= \frac{5 + 5 5 x ^{2}}{2 x}

3 e^{x} x

h \to + 0 - lim (\frac{2 ^{h} - 1}{h})

\int \frac{1}{x ^{2} - 8 x + 25} d x

\frac{d}{d x} (\frac{2 x}{x + 1})

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What is the derivative of f(x)=sqrt(5x)(1+x^2) ?
The derivative of f(x)=sqrt(5x)(1+x^2) is (sqrt(5)+5sqrt(5)x^2)/(2sqrt(x))
What is the first derivative of f(x)=sqrt(5x)(1+x^2) ?
The first derivative of f(x)=sqrt(5x)(1+x^2) is (sqrt(5)+5sqrt(5)x^2)/(2sqrt(x))