What is the derivative of 3csc(x+7cos(x)) ?

The derivative of 3csc(x+7cos(x)) is -3cot(x)csc(x)-7sin(x)

What is the first derivative of 3csc(x+7cos(x)) ?

The first derivative of 3csc(x+7cos(x)) is -3cot(x)csc(x)-7sin(x)

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\frac{d}{d x} (3 csc (x) + 7 cos (x))

- 3 cot (x) csc (x) - 7 sin (x)

Solution steps

\frac{d}{d x} (3 csc (x) + 7 cos (x))

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (3 csc (x)) + \frac{d}{d x} (7 cos (x))

\frac{d}{d x} (3 csc (x)) = - 3 cot (x) csc (x)

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

= - 3 cot (x) csc (x) - 7 sin (x)

What is the derivative of 3csc(x+7cos(x)) ?
The derivative of 3csc(x+7cos(x)) is -3cot(x)csc(x)-7sin(x)
What is the first derivative of 3csc(x+7cos(x)) ?
The first derivative of 3csc(x+7cos(x)) is -3cot(x)csc(x)-7sin(x)