What is the derivative of f(x)=((-7)/(sqrt(7x^2+1))) ?

The derivative of f(x)=((-7)/(sqrt(7x^2+1))) is (49x)/((7x^2+1)^{3/2)}

What is the first derivative of f(x)=((-7)/(sqrt(7x^2+1))) ?

The first derivative of f(x)=((-7)/(sqrt(7x^2+1))) is (49x)/((7x^2+1)^{3/2)}

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derivative of

f (x) = (\frac{- 7}{7 x ^{2} + 1})

\frac{49 x}{( 7 x ^{2} + 1 ) ^{\frac{3}{2}}}

Solution steps

\frac{d}{d x} (\frac{- 7}{7 x ^{2} + 1})

Simplify

\frac{- 7}{7 x ^{2} + 1} : - \frac{7}{7 x ^{2} + 1}

= \frac{d}{d x} (- \frac{7}{7 x ^{2} + 1})

Take the constant out:

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

= - 7 \frac{d}{d x} (\frac{1}{7 x ^{2} + 1})

Apply exponent rule:

\frac{1}{a} = a^{- 1}

= - 7 \frac{d}{d x} ((7 x^{2} + 1)^{- \frac{1}{2}})

Apply the chain rule:

- \frac{1}{2 ( 7 x ^{2} + 1 ) ^{\frac{3}{2}}} \frac{d}{d x} (7 x^{2} + 1)

= - \frac{1}{2 ( 7 x ^{2} + 1 ) ^{\frac{3}{2}}} \frac{d}{d x} (7 x^{2} + 1)

\frac{d}{d x} (7 x^{2} + 1) = 14 x

= - 7 (- \frac{1}{2 ( 7 x ^{2} + 1 ) ^{\frac{3}{2}}} \cdot 14 x)

Simplify

- 7 (- \frac{1}{2 ( 7 x ^{2} + 1 ) ^{\frac{3}{2}}} \cdot 14 x) : \frac{49 x}{( 7 x ^{2} + 1 ) ^{\frac{3}{2}}}

= \frac{49 x}{( 7 x ^{2} + 1 ) ^{\frac{3}{2}}}

x \to 2 lim (\frac{2 + x}{x - 2})

x - 2 x^{2}, - 5 x

y^{^{'}} = t y^{3} - y

x \to - 2 lim ((3 x^{2}) - 6 x + 2)

\int_{- 2}^{2} 1 + 4 x^{2} d x

What is the derivative of f(x)=((-7)/(sqrt(7x^2+1))) ?
The derivative of f(x)=((-7)/(sqrt(7x^2+1))) is (49x)/((7x^2+1)^{3/2)}
What is the first derivative of f(x)=((-7)/(sqrt(7x^2+1))) ?
The first derivative of f(x)=((-7)/(sqrt(7x^2+1))) is (49x)/((7x^2+1)^{3/2)}