What is the derivative of 7/(sin(x+cos(x))) ?

The derivative of 7/(sin(x+cos(x))) is -(7(cos(x)-sin(x)))/(1+sin(2x))

What is the first derivative of 7/(sin(x+cos(x))) ?

The first derivative of 7/(sin(x+cos(x))) is -(7(cos(x)-sin(x)))/(1+sin(2x))

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\frac{d}{d x} (\frac{7}{sin ( x ) + cos ( x )})

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

Solution steps

\frac{d}{d x} (\frac{7}{sin ( x ) + cos ( x )})

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

\frac{d}{d x} (sin (x) + cos (x)) = cos (x) - sin (x)

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

Simplify

7 (- \frac{1}{( sin ( x ) + cos ( x ) ) ^{2}} (cos (x) - sin (x))) : - \frac{7 ( cos ( x ) - sin ( x ) )}{1 + sin ( 2 x )}

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

\int \frac{- cos ( 4 t ) sin ( 4 t )}{4} d t

\int sin^{4} (x) cos^{7} (x) d x

\int 4 x - 11 d x

y^{^{'}} = e^{4 c o s (x)}

2

What is the derivative of 7/(sin(x+cos(x))) ?
The derivative of 7/(sin(x+cos(x))) is -(7(cos(x)-sin(x)))/(1+sin(2x))
What is the first derivative of 7/(sin(x+cos(x))) ?
The first derivative of 7/(sin(x+cos(x))) is -(7(cos(x)-sin(x)))/(1+sin(2x))