What is the derivative of 6^{sin(pix)} ?

The derivative of 6^{sin(pix)} is piln(6)*6^{sin(pix)}cos(pix)

What is the first derivative of 6^{sin(pix)} ?

The first derivative of 6^{sin(pix)} is piln(6)*6^{sin(pix)}cos(pix)

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derivative of

6^{s i n (π x)}

π ln (6) \cdot 6^{s i n (π x)} cos (π x)

Solution steps

\frac{d}{d x} (6^{s i n (π x)})

Apply exponent rule:

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

6^{s i n (π x)} = e^{s i n (π x) l n (6)}

= \frac{d}{d x} (e^{s i n (π x) l n (6)})

Apply the chain rule:

e^{s i n (π x) l n (6)} \frac{d}{d x} (sin (π x) ln (6))

= e^{s i n (π x) l n (6)} \frac{d}{d x} (sin (π x) ln (6))

\frac{d}{d x} (sin (π x) ln (6)) = ln (6) cos (π x) π

= e^{s i n (π x) l n (6)} ln (6) cos (π x) π

e^{s i n (π x) l n (6)} = 6^{s i n (π x)}

= π ln (6) \cdot 6^{s i n (π x)} cos (π x)

\int_{0}^{\infty} t e^{- t} d t

\frac{x}{x ^{2} + 49}

t \to 2 lim (\frac{t ^{2} - 4}{t - 2})

x^{^{'}} + 4 x = t e^{- 4 t}

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

What is the derivative of 6^{sin(pix)} ?
The derivative of 6^{sin(pix)} is piln(6)*6^{sin(pix)}cos(pix)
What is the first derivative of 6^{sin(pix)} ?
The first derivative of 6^{sin(pix)} is piln(6)*6^{sin(pix)}cos(pix)