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

The derivative of (x^2+1/5)sqrt(1+5x^2) is 3xsqrt(1+5x^2)

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

The first derivative of (x^2+1/5)sqrt(1+5x^2) is 3xsqrt(1+5x^2)

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derivative of

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

3 x 1 + 5 x^{2}

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

= 3 x 1 + 5 x^{2}

\int 5 x + 7 d x

f (x) = 5 x + 1

\int sec^{4} (3 x) tan^{3} (3 x) d x

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

x \to 0 lim (\frac{5 x + 1}{x})

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