What is the derivative of 3^{sin(pix}) ?

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

What is the first derivative of 3^{sin(pix}) ?

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

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\frac{d}{d x} (3^{s i n (π x)})

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

Solution steps

\frac{d}{d x} (3^{s i n (π x)})

Apply exponent rule:

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

3^{s i n (π x)} = e^{s i n (π x) l n (3)}

= \frac{d}{d x} (e^{s i n (π x) l n (3)})

Apply the chain rule:

e^{s i n (π x) l n (3)} \frac{d}{d x} (sin (π x) ln (3))

= e^{s i n (π x) l n (3)} \frac{d}{d x} (sin (π x) ln (3))

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

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

e^{s i n (π x) l n (3)} = 3^{s i n (π x)}

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

\frac{d}{d x} ((ln (x))^{7})

\frac{\partial}{\partial x} (6 x^{2} e^{y} - 7 x y^{3})

\int \frac{( 1 + cot ^{2} ( z ) ) cot ( z )}{csc ( z )} d z

\int z e^{y} d y

\frac{d y}{d t} = 1 + t + y + t y

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