What is the derivative of sin((ln(x))^3) ?

The derivative of sin((ln(x))^3) is (3ln^2(x)cos(ln^3(x)))/x

What is the first derivative of sin((ln(x))^3) ?

The first derivative of sin((ln(x))^3) is (3ln^2(x)cos(ln^3(x)))/x

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derivative of

sin ((ln (x))^{3})

\frac{3 ln ^{2} ( x ) cos ( ln ^{3} ( x ) )}{x}

Solution steps

\frac{d}{d x} (sin ((ln (x))^{3}))

Apply the chain rule:

cos ((ln (x))^{3}) \frac{d}{d x} ((ln (x))^{3})

= cos ((ln (x))^{3}) \frac{d}{d x} ((ln (x))^{3})

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

= cos ((ln (x))^{3}) \frac{3 ln ^{2} ( x )}{x}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{3 ln ^{2} ( x ) cos ( ln ^{3} ( x ) )}{x}

\frac{3 x ^{2} tan ( x )}{sec ( x )}

\frac{d}{d n} (\frac{2 ^{n}}{n !})

y = - 3^{2} + x + 2

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

ln ((2 x - 3)^{2})

What is the derivative of sin((ln(x))^3) ?
The derivative of sin((ln(x))^3) is (3ln^2(x)cos(ln^3(x)))/x
What is the first derivative of sin((ln(x))^3) ?
The first derivative of sin((ln(x))^3) is (3ln^2(x)cos(ln^3(x)))/x