What is the derivative of tan^{x^2}(x) ?

The derivative of tan^{x^2}(x) is tan^{x^2}(x)(2xln(tan(x))+2x^2csc(2x))

What is the first derivative of tan^{x^2}(x) ?

The first derivative of tan^{x^2}(x) is tan^{x^2}(x)(2xln(tan(x))+2x^2csc(2x))

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

tan^{x^{2}} (x) (2 x ln (tan (x)) + 2 x^{2} csc (2 x))

Solution steps

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

Apply exponent rule:

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

tan^{x^{2}} (x) = e^{x^{2} l n (t a n (x))}

= \frac{d}{d x} (e^{x^{2} l n (t a n (x))})

Apply the chain rule:

e^{x^{2} l n (t a n (x))} \frac{d}{d x} (x^{2} ln (tan (x)))

= e^{x^{2} l n (t a n (x))} \frac{d}{d x} (x^{2} ln (tan (x)))

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

= e^{x^{2} l n (t a n (x))} (2 x ln (tan (x)) + 2 csc (2 x) x^{2})

e^{x^{2} l n (t a n (x))} = tan^{x^{2}} (x)

= tan^{x^{2}} (x) (2 x ln (tan (x)) + 2 x^{2} csc (2 x))

\frac{e ^{t}}{t}

\int x cos (\frac{mπ x}{2}) d x

\frac{d}{d x} ((\frac{3}{5})^{x})

\int sec (t) (4 sec (t) + 7 tan (t)) d t

\frac{d}{d y} (y e^{x})

What is the derivative of tan^{x^2}(x) ?
The derivative of tan^{x^2}(x) is tan^{x^2}(x)(2xln(tan(x))+2x^2csc(2x))
What is the first derivative of tan^{x^2}(x) ?
The first derivative of tan^{x^2}(x) is tan^{x^2}(x)(2xln(tan(x))+2x^2csc(2x))