What is the derivative of 10^{tan(piθ)} ?

The derivative of 10^{tan(piθ)} is piln(10)*10^{tan(piθ)}sec^2(piθ)

What is the first derivative of 10^{tan(piθ)} ?

The first derivative of 10^{tan(piθ)} is piln(10)*10^{tan(piθ)}sec^2(piθ)

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derivative of

1 0^{t a n (π θ)}

π ln (10) \cdot 1 0^{t a n (π θ)} sec^{2} (π θ)

Solution steps

\frac{d}{d θ} (1 0^{t a n (π θ)})

Apply exponent rule:

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

1 0^{t a n (π θ)} = e^{t a n (π θ) l n (10)}

= \frac{d}{d θ} (e^{t a n (π θ) l n (10)})

Apply the chain rule:

e^{t a n (π θ) l n (10)} \frac{d}{d θ} (tan (π θ) ln (10))

= e^{t a n (π θ) l n (10)} \frac{d}{d θ} (tan (π θ) ln (10))

\frac{d}{d θ} (tan (π θ) ln (10)) = ln (10) sec^{2} (π θ) π

= e^{t a n (π θ) l n (10)} ln (10) sec^{2} (π θ) π

e^{t a n (π θ) l n (10)} = 1 0^{t a n (π θ)}

= π ln (10) \cdot 1 0^{t a n (π θ)} sec^{2} (π θ)

f (x) = tan (2 x)

\int - 4 sin^{3} (x) cos^{5} (x) d x

y = x^{2} - 4 x + 1, y = x + 1

x \to 0 lim (\frac{- x ^{- x} - 1}{x})

\frac{d}{d x} (\frac{e ^{- x}}{x - 5} + 1)

What is the derivative of 10^{tan(piθ)} ?
The derivative of 10^{tan(piθ)} is piln(10)*10^{tan(piθ)}sec^2(piθ)
What is the first derivative of 10^{tan(piθ)} ?
The first derivative of 10^{tan(piθ)} is piln(10)*10^{tan(piθ)}sec^2(piθ)