What is the derivative of (cosh(x)/(sin^2(x))) ?

The derivative of (cosh(x)/(sin^2(x))) is -2csc^2(x)cot(x)cosh(x)+csc^2(x)sinh(x)

What is the first derivative of (cosh(x)/(sin^2(x))) ?

The first derivative of (cosh(x)/(sin^2(x))) is -2csc^2(x)cot(x)cosh(x)+csc^2(x)sinh(x)

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\frac{d}{d x} (\frac{cosh ( x )}{sin ^{2} ( x )})

- 2 csc^{2} (x) cot (x) cosh (x) + csc^{2} (x) sinh (x)

Solution steps

\frac{d}{d x} (\frac{cosh ( x )}{sin ^{2} ( x )})

Simplify

\frac{cosh ( x )}{sin ^{2} ( x )} : csc^{2} (x) cosh (x)

= \frac{d}{d x} (csc^{2} (x) cosh (x))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = csc^{2} (x), g = cosh (x)

= \frac{d}{d x} (csc^{2} (x)) cosh (x) + \frac{d}{d x} (cosh (x)) csc^{2} (x)

\frac{d}{d x} (csc^{2} (x)) = - 2 csc^{2} (x) cot (x)

\frac{d}{d x} (cosh (x)) = sinh (x)

= (- 2 csc^{2} (x) cot (x)) cosh (x) + sinh (x) csc^{2} (x)

Simplify

= - 2 csc^{2} (x) cot (x) cosh (x) + csc^{2} (x) sinh (x)

\frac{d}{d x} (5 cos (5 x))

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

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

y = 2 - x^{2}

\int_{- 2 π}^{π} π sin^{2} (x) d x

What is the derivative of (cosh(x)/(sin^2(x))) ?
The derivative of (cosh(x)/(sin^2(x))) is -2csc^2(x)cot(x)cosh(x)+csc^2(x)sinh(x)
What is the first derivative of (cosh(x)/(sin^2(x))) ?
The first derivative of (cosh(x)/(sin^2(x))) is -2csc^2(x)cot(x)cosh(x)+csc^2(x)sinh(x)