What is the derivative of ln(x^4+cot(3x)) ?

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

What is the first derivative of ln(x^4+cot(3x)) ?

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

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

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

Solution steps

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

Apply the chain rule:

\frac{1}{x ^{4} + cot ( 3 x )} \frac{d}{d x} (x^{4} + cot (3 x))

= \frac{1}{x ^{4} + cot ( 3 x )} \frac{d}{d x} (x^{4} + cot (3 x))

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

= \frac{1}{x ^{4} + cot ( 3 x )} (4 x^{3} - csc^{2} (3 x) \cdot 3)

Simplify

\frac{1}{x ^{4} + cot ( 3 x )} (4 x^{3} - csc^{2} (3 x) \cdot 3) : \frac{4 x ^{3} - 3 csc ^{2} ( 3 x )}{x ^{4} + cot ( 3 x )}

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

sin^{2} (e^{s i n (2) (t)})

\frac{d}{d x} (2 cos^{4} (x))

f (x) = \frac{x ^{2} + 1}{x}

\int \frac{1}{e ^{x} - 4 e ^{- x}} d x

y^{^{'}} = \frac{( y ^{4} - 1 )}{4 x y ^{3}}

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