What is the derivative of 2^{sin(pix)} ?

The derivative of 2^{sin(pix)} is piln(2)*2^{sin(pix)}cos(pix)

What is the first derivative of 2^{sin(pix)} ?

The first derivative of 2^{sin(pix)} is piln(2)*2^{sin(pix)}cos(pix)

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derivative of

2^{s i n (π x)}

π ln (2) \cdot 2^{s i n (π x)} cos (π x)

Solution steps

\frac{d}{d x} (2^{s i n (π x)})

Apply exponent rule:

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

2^{s i n (π x)} = e^{s i n (π x) l n (2)}

= \frac{d}{d x} (e^{s i n (π x) l n (2)})

Apply the chain rule:

e^{s i n (π x) l n (2)} \frac{d}{d x} (sin (π x) ln (2))

= e^{s i n (π x) l n (2)} \frac{d}{d x} (sin (π x) ln (2))

\frac{d}{d x} (sin (π x) ln (2)) = ln (2) cos (π x) π

= e^{s i n (π x) l n (2)} ln (2) cos (π x) π

e^{s i n (π x) l n (2)} = 2^{s i n (π x)}

= π ln (2) \cdot 2^{s i n (π x)} cos (π x)

\frac{\partial}{\partial x} (\frac{x}{x ^{2} + x + 1})

(\frac{6 x ^{2}}{6 - x})^{3}

\int \frac{( 1 - x ) y}{x}

x \to 0 lim (∣ 5 x ∣)

\frac{d}{d x} (\frac{1}{3 2 x - 1})

What is the derivative of 2^{sin(pix)} ?
The derivative of 2^{sin(pix)} is piln(2)*2^{sin(pix)}cos(pix)
What is the first derivative of 2^{sin(pix)} ?
The first derivative of 2^{sin(pix)} is piln(2)*2^{sin(pix)}cos(pix)