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Popular Calculus >

derivative of y=11^{tan(6x)}

Solution

derivative of

y = 1 1^{t a n (6 x)}

Solution

e^{t a n (6 x) l n (11)} ln (11) sec^{2} (6 x) \cdot 6

Solution steps

\frac{d}{d x} (1 1^{t a n (6 x)})

Apply exponent rule:

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

1 1^{t a n (6 x)} = e^{t a n (6 x) l n (11)}

= \frac{d}{d x} (e^{t a n (6 x) l n (11)})

Apply the chain rule:

e^{t a n (6 x) l n (11)} \frac{d}{d x} (tan (6 x) ln (11))

= e^{t a n (6 x) l n (11)} \frac{d}{d x} (tan (6 x) ln (11))

\frac{d}{d x} (tan (6 x) ln (11)) = ln (11) sec^{2} (6 x) \cdot 6

= e^{t a n (6 x) l n (11)} ln (11) sec^{2} (6 x) \cdot 6

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of y=11^{tan(6x)} ?
The derivative of y=11^{tan(6x)} is e^{tan(6x)ln(11)}ln(11)sec^2(6x)*6
What is the first derivative of y=11^{tan(6x)} ?
The first derivative of y=11^{tan(6x)} is e^{tan(6x)ln(11)}ln(11)sec^2(6x)*6