What is the derivative of (tan(x)^{7/x}) ?

The derivative of (tan(x)^{7/x}) is 7tan^{7/x}(x)(-(ln(tan(x))}{x^2}+\frac{2csc(2x))/x)

What is the first derivative of (tan(x)^{7/x}) ?

The first derivative of (tan(x)^{7/x}) is 7tan^{7/x}(x)(-(ln(tan(x))}{x^2}+\frac{2csc(2x))/x)

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\frac{d}{d x} ((tan (x))^{\frac{7}{x}})

7 tan^{\frac{7}{x}} (x) (- \frac{ln ( tan ( x ) )}{x ^{2}} + \frac{2 csc ( 2 x )}{x})

Solution steps

\frac{d}{d x} ((tan (x))^{\frac{7}{x}})

Apply exponent rule:

a^{b} = e^{b l n (a)}

(tan (x))^{\frac{7}{x}} = e^{\frac{7}{x} l n (t a n (x))}

= \frac{d}{d x} (e^{\frac{7}{x} l n (t a n (x))})

Apply the chain rule:

e^{\frac{7}{x} l n (t a n (x))} \frac{d}{d x} (\frac{7}{x} ln (tan (x)))

= e^{\frac{7}{x} l n (t a n (x))} \frac{d}{d x} (\frac{7}{x} ln (tan (x)))

\frac{d}{d x} (\frac{7}{x} ln (tan (x))) = 7 (- \frac{ln ( tan ( x ) )}{x ^{2}} + \frac{2 csc ( 2 x )}{x})

= e^{\frac{7}{x} l n (t a n (x))} \cdot 7 (- \frac{ln ( tan ( x ) )}{x ^{2}} + \frac{2 csc ( 2 x )}{x})

e^{\frac{7}{x} l n (t a n (x))} = tan^{\frac{7}{x}} (x)

= 7 tan^{\frac{7}{x}} (x) (- \frac{ln ( tan ( x ) )}{x ^{2}} + \frac{2 csc ( 2 x )}{x})

y^{^{'}} - x y = 2 x y

\frac{1}{4} (70 x^{2} - 8 x^{3})

\int_{0}^{π} cos (x) d x

\frac{\partial}{\partial x} (y^{2} sin (2 x y))

x \to - 3 lim (\frac{x + 2}{x ^{2} - 9})

What is the derivative of (tan(x)^{7/x}) ?
The derivative of (tan(x)^{7/x}) is 7tan^{7/x}(x)(-(ln(tan(x))}{x^2}+\frac{2csc(2x))/x)
What is the first derivative of (tan(x)^{7/x}) ?
The first derivative of (tan(x)^{7/x}) is 7tan^{7/x}(x)(-(ln(tan(x))}{x^2}+\frac{2csc(2x))/x)