What is the derivative of sqrt(sin(7x+ln(5x))) ?

The derivative of sqrt(sin(7x+ln(5x))) is (cos(7x+ln(5x))(7x+1))/(2xsqrt(sin(7x+ln(5x))))

What is the first derivative of sqrt(sin(7x+ln(5x))) ?

The first derivative of sqrt(sin(7x+ln(5x))) is (cos(7x+ln(5x))(7x+1))/(2xsqrt(sin(7x+ln(5x))))

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\frac{d}{d x} (sin (7 x + ln (5 x)))

\frac{cos ( 7 x + ln ( 5 x ) ) ( 7 x + 1 )}{2 x sin ( 7 x + ln ( 5 x ) )}

Solution steps

\frac{d}{d x} (sin (7 x + ln (5 x)))

Apply the chain rule:

\frac{1}{2 sin ( 7 x + ln ( 5 x ) )} \frac{d}{d x} (sin (7 x + ln (5 x)))

= \frac{1}{2 sin ( 7 x + ln ( 5 x ) )} \frac{d}{d x} (sin (7 x + ln (5 x)))

\frac{d}{d x} (sin (7 x + ln (5 x))) = cos (7 x + ln (5 x)) (7 + \frac{1}{x})

= \frac{1}{2 sin ( 7 x + ln ( 5 x ) )} cos (7 x + ln (5 x)) (7 + \frac{1}{x})

Simplify

\frac{1}{2 sin ( 7 x + ln ( 5 x ) )} cos (7 x + ln (5 x)) (7 + \frac{1}{x}) : \frac{cos ( 7 x + ln ( 5 x ) ) ( 7 x + 1 )}{2 x sin ( 7 x + ln ( 5 x ) )}

= \frac{cos ( 7 x + ln ( 5 x ) ) ( 7 x + 1 )}{2 x sin ( 7 x + ln ( 5 x ) )}

x \to 0 lim (\frac{1}{x ^{2} ( x + 7 )})

t \cdot cos (k t)

\int \frac{1}{9 x - 4} d x

\int \frac{x ^{2} - 2 x}{x ^{3} - 3 x ^{2} + 1} d x

\frac{d}{d x} (e^{s i n (x)} \cdot cos (sin (x)))

What is the derivative of sqrt(sin(7x+ln(5x))) ?
The derivative of sqrt(sin(7x+ln(5x))) is (cos(7x+ln(5x))(7x+1))/(2xsqrt(sin(7x+ln(5x))))
What is the first derivative of sqrt(sin(7x+ln(5x))) ?
The first derivative of sqrt(sin(7x+ln(5x))) is (cos(7x+ln(5x))(7x+1))/(2xsqrt(sin(7x+ln(5x))))