What is the derivative of y=-csc(x)-sin(x) ?

The derivative of y=-csc(x)-sin(x) is cot^2(x)cos(x)

What is the first derivative of y=-csc(x)-sin(x) ?

The first derivative of y=-csc(x)-sin(x) is cot^2(x)cos(x)

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derivative of

y = - csc (x) - sin (x)

cot^{2} (x) cos (x)

Solution steps

\frac{d}{d x} (- csc (x) - sin (x))

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= - \frac{d}{d x} (csc (x)) - \frac{d}{d x} (sin (x))

\frac{d}{d x} (csc (x)) = - cot (x) csc (x)

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

= - (- cot (x) csc (x)) - cos (x)

Simplify

- (- cot (x) csc (x)) - cos (x) : cot^{2} (x) cos (x)

= cot^{2} (x) cos (x)

y^{^{''}} - 4 y^{^{'}} - 5 y = - 3 e^{4} t, y (0) = 0, y^{^{'}} (0) = 0

\int_{1}^{x} (\frac{1}{t ^{3} + 1}) d t

\int \frac{1}{sec ( a x ) + 1} d x

\frac{d y}{d x} = \frac{( ( 4 x ) sec ( \frac{y}{x} ) + y )}{x}

y^{^{'}} = \frac{( y ^{2} )}{x ^{3}}

What is the derivative of y=-csc(x)-sin(x) ?
The derivative of y=-csc(x)-sin(x) is cot^2(x)cos(x)
What is the first derivative of y=-csc(x)-sin(x) ?
The first derivative of y=-csc(x)-sin(x) is cot^2(x)cos(x)