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Popular >

derivative of f(x)=-tan(x)-5cot(x)

Solution

derivative of

f (x) = - tan (x) - 5 cot (x)

Solution

- sec^{2} (x) + 5 csc^{2} (x)

Solution steps

\frac{d}{d x} (- tan (x) - 5 cot (x))

Apply the Sum/Difference Rule:

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

= - \frac{d}{d x} (tan (x)) - \frac{d}{d x} (5 cot (x))

\frac{d}{d x} (tan (x)) = sec^{2} (x)

\frac{d}{d x} (5 cot (x)) = - 5 csc^{2} (x)

= - sec^{2} (x) - (- 5 csc^{2} (x))

Simplify

= - sec^{2} (x) + 5 csc^{2} (x)

Popular Examples

derivative of x(x-1^3)

\frac{d}{d x} (x (x - 1)^{3})

integral of-x^2(x+1)^3(x-1)

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

(\partial)/(\partial y)(x^2+2y^2)

\frac{\partial}{\partial y} (x^{2} + 2 y^{2})

derivative of arctan((1-x/(1+x)))

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

integral from 0 to 3 of (-x^2+x-1)

\int_{0}^{3} (- x^{2} + x - 1) d x

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=-tan(x)-5cot(x) ?
The derivative of f(x)=-tan(x)-5cot(x) is -sec^2(x)+5csc^2(x)
What is the first derivative of f(x)=-tan(x)-5cot(x) ?
The first derivative of f(x)=-tan(x)-5cot(x) is -sec^2(x)+5csc^2(x)