What is the derivative of sqrt(5+4{f)(x}) ?

The derivative of sqrt(5+4{f)(x}) is (2 derivative of {f}(x))/(sqrt(5+4{f)(x))}

What is the first derivative of sqrt(5+4{f)(x}) ?

The first derivative of sqrt(5+4{f)(x}) is (2 derivative of {f}(x))/(sqrt(5+4{f)(x))}

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\frac{d}{d x} (5 + 4 f (x))

\frac{2 \frac{d}{d x} ( f ( x ) )}{5 + 4 f ( x )}

Solution steps

\frac{d}{d x} (5 + 4 f (x))

Apply the chain rule:

\frac{1}{2 5 + 4 f ( x )} \frac{d}{d x} (5 + 4 f (x))

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

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

= \frac{1}{2 5 + 4 f ( x )} \cdot 4 \frac{d}{d x} (f (x))

Simplify

\frac{1}{2 5 + 4 f ( x )} \cdot 4 \frac{d}{d x} (f (x)) : \frac{2 \frac{d}{d x} ( f ( x ) )}{5 + 4 f ( x )}

= \frac{2 \frac{d}{d x} ( f ( x ) )}{5 + 4 f ( x )}

\int 5 x^{4} sin^{2} (x^{5}) d x

\frac{d y}{d x} = e^{2 x - 5 y}

y^{^{'}} = \frac{x ^{2} + 2 y ^{2}}{x y}

y^{^{''}} - y^{^{'}} - 30 = 0

569 + t (37 t^{0.6} - 108)

What is the derivative of sqrt(5+4{f)(x}) ?
The derivative of sqrt(5+4{f)(x}) is (2 derivative of {f}(x))/(sqrt(5+4{f)(x))}
What is the first derivative of sqrt(5+4{f)(x}) ?
The first derivative of sqrt(5+4{f)(x}) is (2 derivative of {f}(x))/(sqrt(5+4{f)(x))}