What is the derivative of 8^{sin(pix}) ?

The derivative of 8^{sin(pix}) is 3piln(2)*8^{sin(pix)}cos(pix)

What is the first derivative of 8^{sin(pix}) ?

The first derivative of 8^{sin(pix}) is 3piln(2)*8^{sin(pix)}cos(pix)

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\frac{d}{d x} (8^{s i n (π x)})

3 π ln (2) \cdot 8^{s i n (π x)} cos (π x)

Solution steps

\frac{d}{d x} (8^{s i n (π x)})

Apply exponent rule:

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

8^{s i n (π x)} = e^{s i n (π x) l n (8)}

= \frac{d}{d x} (e^{s i n (π x) l n (8)})

Apply the chain rule:

e^{s i n (π x) l n (8)} \frac{d}{d x} (sin (π x) ln (8))

= e^{s i n (π x) l n (8)} \frac{d}{d x} (sin (π x) ln (8))

\frac{d}{d x} (sin (π x) ln (8)) = 3 ln (2) cos (π x) π

= e^{s i n (π x) l n (8)} \cdot 3 ln (2) cos (π x) π

e^{s i n (π x) l n (8)} = 8^{s i n (π x)}

= 3 π ln (2) \cdot 8^{s i n (π x)} cos (π x)

\int_{1}^{8} \frac{2}{x} d x

f (x) = - 6

x \to - 6 lim (\frac{1}{x + 6})

\frac{\partial}{\partial x} (4 x^{3} y^{2} + 4)

f (x) = 3 x^{4}

What is the derivative of 8^{sin(pix}) ?
The derivative of 8^{sin(pix}) is 3piln(2)*8^{sin(pix)}cos(pix)
What is the first derivative of 8^{sin(pix}) ?
The first derivative of 8^{sin(pix}) is 3piln(2)*8^{sin(pix)}cos(pix)