What is the derivative of 9^{sin(pix}) ?

The derivative of 9^{sin(pix}) is 2piln(3)*9^{sin(pix)}cos(pix)

What is the first derivative of 9^{sin(pix}) ?

The first derivative of 9^{sin(pix}) is 2piln(3)*9^{sin(pix)}cos(pix)

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\frac{d}{d x} (9^{s i n (π x)})

2 π ln (3) \cdot 9^{s i n (π x)} cos (π x)

Solution steps

\frac{d}{d x} (9^{s i n (π x)})

Apply exponent rule:

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

9^{s i n (π x)} = e^{s i n (π x) l n (9)}

= \frac{d}{d x} (e^{s i n (π x) l n (9)})

Apply the chain rule:

e^{s i n (π x) l n (9)} \frac{d}{d x} (sin (π x) ln (9))

= e^{s i n (π x) l n (9)} \frac{d}{d x} (sin (π x) ln (9))

\frac{d}{d x} (sin (π x) ln (9)) = 2 ln (3) cos (π x) π

= e^{s i n (π x) l n (9)} \cdot 2 ln (3) cos (π x) π

e^{s i n (π x) l n (9)} = 9^{s i n (π x)}

= 2 π ln (3) \cdot 9^{s i n (π x)} cos (π x)

\frac{d}{d x} (- sin (x) + cos (x) + x - \frac{1}{x ^{2}})

f (x) = x + 7, at x = 9

\int tan (θ) 4 sin (2 θ) d θ

\int \frac{7}{( z - 10 ) ^{7}} d z

\int_{- 1}^{1} 3^{x} d x

What is the derivative of 9^{sin(pix}) ?
The derivative of 9^{sin(pix}) is 2piln(3)*9^{sin(pix)}cos(pix)
What is the first derivative of 9^{sin(pix}) ?
The first derivative of 9^{sin(pix}) is 2piln(3)*9^{sin(pix)}cos(pix)