What is the derivative of sqrt(7+6f(x)) ?

The derivative of sqrt(7+6f(x)) is (3x)/(sqrt(7+6fx))

What is the first derivative of sqrt(7+6f(x)) ?

The first derivative of sqrt(7+6f(x)) is (3x)/(sqrt(7+6fx))

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derivative of

7 + 6 f (x)

\frac{3 x}{7 + 6 f x}

Solution steps

\frac{d}{df} (7 + 6 f x)

Treat

x

as a constant

Apply the chain rule:

\frac{1}{2 7 + 6 f x} \frac{d}{df} (7 + 6 f x)

= \frac{1}{2 7 + 6 f x} \frac{d}{df} (7 + 6 f x)

\frac{d}{df} (7 + 6 f x) = 6 x

= \frac{1}{2 7 + 6 f x} \cdot 6 x

Simplify

\frac{1}{2 7 + 6 f x} \cdot 6 x : \frac{3 x}{7 + 6 f x}

= \frac{3 x}{7 + 6 f x}

\int \frac{x}{x ^{2} - 2 x + 5} d x

\frac{\partial}{\partial y} (x^{3} y e^{x y})

y = \frac{7}{x ^{2} + 3}

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

\int \frac{3}{x x ^{2} - 9} d x

What is the derivative of sqrt(7+6f(x)) ?
The derivative of sqrt(7+6f(x)) is (3x)/(sqrt(7+6fx))
What is the first derivative of sqrt(7+6f(x)) ?
The first derivative of sqrt(7+6f(x)) is (3x)/(sqrt(7+6fx))