What is the derivative of sqrt(6+5{f)(x}) ?

The derivative of sqrt(6+5{f)(x}) is (5 derivative of {f}(x))/(2sqrt(6+5{f)(x))}

What is the first derivative of sqrt(6+5{f)(x}) ?

The first derivative of sqrt(6+5{f)(x}) is (5 derivative of {f}(x))/(2sqrt(6+5{f)(x))}

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\frac{d}{d x} (6 + 5 f (x))

\frac{5 \frac{d}{d x} ( f ( x ) )}{2 6 + 5 f ( x )}

Solution steps

\frac{d}{d x} (6 + 5 f (x))

Apply the chain rule:

\frac{1}{2 6 + 5 f ( x )} \frac{d}{d x} (6 + 5 f (x))

= \frac{1}{2 6 + 5 f ( x )} \frac{d}{d x} (6 + 5 f (x))

\frac{d}{d x} (6 + 5 f (x)) = 5 \frac{d}{d x} (f (x))

= \frac{1}{2 6 + 5 f ( x )} \cdot 5 \frac{d}{d x} (f (x))

Simplify

\frac{1}{2 6 + 5 f ( x )} \cdot 5 \frac{d}{d x} (f (x)) : \frac{5 \frac{d}{d x} ( f ( x ) )}{2 6 + 5 f ( x )}

= \frac{5 \frac{d}{d x} ( f ( x ) )}{2 6 + 5 f ( x )}

\int_{0.1}^{0.2} 600 x d x

x \to \infty lim (x - 3)

\int \frac{1}{cos ^{2} ( θ )} d θ

y = e^{x} x^{5} + 10 e^{x} x^{4} + 20 e^{x} x^{3}

\frac{d y}{d t} = 0.225 - \frac{y}{200}

What is the derivative of sqrt(6+5{f)(x}) ?
The derivative of sqrt(6+5{f)(x}) is (5 derivative of {f}(x))/(2sqrt(6+5{f)(x))}
What is the first derivative of sqrt(6+5{f)(x}) ?
The first derivative of sqrt(6+5{f)(x}) is (5 derivative of {f}(x))/(2sqrt(6+5{f)(x))}