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

The derivative of (x^x/(sin(x))) is x^xcsc(x)(ln(x)+1)-x^xcot(x)csc(x)

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

The first derivative of (x^x/(sin(x))) is x^xcsc(x)(ln(x)+1)-x^xcot(x)csc(x)

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

x^{x} csc (x) (ln (x) + 1) - x^{x} cot (x) csc (x)

Solution steps

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

Simplify

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

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

Apply the Product Rule:

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

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

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

\frac{d}{d x} (x^{x}) = x^{x} (ln (x) + 1)

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

= x^{x} (ln (x) + 1) csc (x) + (- cot (x) csc (x)) x^{x}

Simplify

= x^{x} csc (x) (ln (x) + 1) - x^{x} cot (x) csc (x)

\frac{d y}{d x} = k \cdot y^{2}

\frac{d y}{d x} = \frac{1}{1 + x}

d er i v a t i v e f (x) = - 12 x^{2} + 400 x - 3800

t an g e n t 3 x - 4 x^{2}

\int (1 - sin^{2} (x)) cos (x) d x

What is the derivative of (x^x/(sin(x))) ?
The derivative of (x^x/(sin(x))) is x^xcsc(x)(ln(x)+1)-x^xcot(x)csc(x)
What is the first derivative of (x^x/(sin(x))) ?
The first derivative of (x^x/(sin(x))) is x^xcsc(x)(ln(x)+1)-x^xcot(x)csc(x)