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Popular Calculus >

derivative of f(x)=sin(x)+3/4 cot(x)

Solution

derivative of

f (x) = sin (x) + \frac{3}{4} cot (x)

Solution

cos (x) - \frac{3}{4} csc^{2} (x)

Solution steps

\frac{d}{d x} (sin (x) + \frac{3}{4} cot (x))

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (sin (x)) + \frac{d}{d x} (\frac{3}{4} cot (x))

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

\frac{d}{d x} (\frac{3}{4} cot (x)) = - \frac{3}{4} csc^{2} (x)

= cos (x) - \frac{3}{4} csc^{2} (x)

Graph

Popular Examples

derivative of (1+7/x ^5)

\frac{d}{d x} ((1 + \frac{7}{x})^{5})

limit as x approaches-3 of sqrt(5x^2+2x)

x \to - 3 lim (5 x^{2} + 2 x)

integral of (1+x)/(1-\sqrt[3]{x)}

\int \frac{1 + x}{1 - 3 x} d x

limit as x approaches 3 of (x-2)/(x-3)

x \to 3 lim (\frac{x - 2}{x - 3})

integral of 3/(4(4-3x)^7)

\int \frac{3}{4 ( 4 - 3 x ) ^{7}} d x

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=sin(x)+3/4 cot(x) ?
The derivative of f(x)=sin(x)+3/4 cot(x) is cos(x)-3/4 csc^2(x)
What is the first derivative of f(x)=sin(x)+3/4 cot(x) ?
The first derivative of f(x)=sin(x)+3/4 cot(x) is cos(x)-3/4 csc^2(x)