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Popular >

derivative of x^3csc(x)

Solution

derivative of

x^{3} csc (x)

Solution

3 x^{2} csc (x) - x^{3} cot (x) csc (x)

Solution steps

\frac{d}{d x} (x^{3} csc (x))

Apply the Product Rule:

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

f = x^{3}, g = csc (x)

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

\frac{d}{d x} (x^{3}) = 3 x^{2}

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

= 3 x^{2} csc (x) + (- cot (x) csc (x)) x^{3}

Simplify

= 3 x^{2} csc (x) - x^{3} cot (x) csc (x)

Popular Examples

derivative of ln((ln(x)^2))

\frac{d}{d x} (ln ((ln (x))^{2}))

integral of (1-sin^3(x))/(sin^2(x))

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

derivative of (2x^2-3x+1/x)

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

slope of x^2+xy+2y^2=28,(2,3)slope

x^{2} + x y + 2 y^{2} = 28, (2, 3)

t^2y^{''}+7ty^'+10y=0

t^{2} y^{^{''}} + 7 t y^{^{'}} + 10 y = 0

Frequently Asked Questions (FAQ)

What is the derivative of x^3csc(x) ?
The derivative of x^3csc(x) is 3x^2csc(x)-x^3cot(x)csc(x)
What is the first derivative of x^3csc(x) ?
The first derivative of x^3csc(x) is 3x^2csc(x)-x^3cot(x)csc(x)