What is the derivative of (9x)^{csc(6x)} ?

The derivative of (9x)^{csc(6x)} is (-6cot(6x)csc(6x)ln(9x)+(csc(6x))/x)(9x)^{csc(6x)}

What is the first derivative of (9x)^{csc(6x)} ?

The first derivative of (9x)^{csc(6x)} is (-6cot(6x)csc(6x)ln(9x)+(csc(6x))/x)(9x)^{csc(6x)}

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derivative of

(9 x)^{c s c (6 x)}

(- 6 cot (6 x) csc (6 x) ln (9 x) + \frac{csc ( 6 x )}{x}) (9 x)^{c s c (6 x)}

Solution steps

\frac{d}{d x} ((9 x)^{c s c (6 x)})

Apply exponent rule:

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

(9 x)^{c s c (6 x)} = e^{c s c (6 x) l n (9 x)}

= \frac{d}{d x} (e^{c s c (6 x) l n (9 x)})

Apply the chain rule:

e^{c s c (6 x) l n (9 x)} \frac{d}{d x} (csc (6 x) ln (9 x))

= e^{c s c (6 x) l n (9 x)} \frac{d}{d x} (csc (6 x) ln (9 x))

\frac{d}{d x} (csc (6 x) ln (9 x)) = - 6 cot (6 x) csc (6 x) ln (9 x) + \frac{csc ( 6 x )}{x}

= e^{c s c (6 x) l n (9 x)} (- 6 cot (6 x) csc (6 x) ln (9 x) + \frac{csc ( 6 x )}{x})

e^{c s c (6 x) l n (9 x)} = (9 x)^{c s c (6 x)}

= (- 6 cot (6 x) csc (6 x) ln (9 x) + \frac{csc ( 6 x )}{x}) (9 x)^{c s c (6 x)}

\int \frac{sin ( in x )}{x} d x

\int 8 cos (3 x) d x

4 + 7 x + x^{2} + δ

x \to 0 lim (\frac{7 x ^{2}}{x ^{2}})

x \to 5 lim (75)

What is the derivative of (9x)^{csc(6x)} ?
The derivative of (9x)^{csc(6x)} is (-6cot(6x)csc(6x)ln(9x)+(csc(6x))/x)(9x)^{csc(6x)}
What is the first derivative of (9x)^{csc(6x)} ?
The first derivative of (9x)^{csc(6x)} is (-6cot(6x)csc(6x)ln(9x)+(csc(6x))/x)(9x)^{csc(6x)}