What is the derivative of (3x^4/(tan(x))) ?

The derivative of (3x^4/(tan(x))) is 3(4x^3cot(x)-x^4csc^2(x))

What is the first derivative of (3x^4/(tan(x))) ?

The first derivative of (3x^4/(tan(x))) is 3(4x^3cot(x)-x^4csc^2(x))

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\frac{d}{d x} (\frac{3 x ^{4}}{tan ( x )})

3 (4 x^{3} cot (x) - x^{4} csc^{2} (x))

Solution steps

\frac{d}{d x} (\frac{3 x ^{4}}{tan ( x )})

Simplify

\frac{3 x ^{4}}{tan ( x )} : 3 x^{4} cot (x)

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Product Rule:

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

f = x^{4}, g = cot (x)

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

\frac{d}{d x} (x^{4}) = 4 x^{3}

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

= 3 (4 x^{3} cot (x) + (- csc^{2} (x)) x^{4})

Simplify

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

5^{2 x}

\frac{d}{d x} (\frac{q x + r}{s x + r})

x \to 0 + lim (\frac{- ln ( 1 + 6 x )}{x})

3 x

\frac{\partial}{\partial x} (x^{2} + 4 y^{2})

What is the derivative of (3x^4/(tan(x))) ?
The derivative of (3x^4/(tan(x))) is 3(4x^3cot(x)-x^4csc^2(x))
What is the first derivative of (3x^4/(tan(x))) ?
The first derivative of (3x^4/(tan(x))) is 3(4x^3cot(x)-x^4csc^2(x))