What is the derivative of 10^{sin(pix}) ?

The derivative of 10^{sin(pix}) is piln(10)*10^{sin(pix)}cos(pix)

What is the first derivative of 10^{sin(pix}) ?

The first derivative of 10^{sin(pix}) is piln(10)*10^{sin(pix)}cos(pix)

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\frac{d}{d x} (1 0^{s i n (π x)})

π ln (10) \cdot 1 0^{s i n (π x)} cos (π x)

Solution steps

\frac{d}{d x} (1 0^{s i n (π x)})

Apply exponent rule:

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

1 0^{s i n (π x)} = e^{s i n (π x) l n (10)}

= \frac{d}{d x} (e^{s i n (π x) l n (10)})

Apply the chain rule:

e^{s i n (π x) l n (10)} \frac{d}{d x} (sin (π x) ln (10))

= e^{s i n (π x) l n (10)} \frac{d}{d x} (sin (π x) ln (10))

\frac{d}{d x} (sin (π x) ln (10)) = ln (10) cos (π x) π

= e^{s i n (π x) l n (10)} ln (10) cos (π x) π

e^{s i n (π x) l n (10)} = 1 0^{s i n (π x)}

= π ln (10) \cdot 1 0^{s i n (π x)} cos (π x)

\int \frac{x}{16 - 9 x ^{2}} d x

\int 4 x^{3} e^{- x^{2}} d x

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

\int sin^{3} (x) cos^{18} (x) d x

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

What is the derivative of 10^{sin(pix}) ?
The derivative of 10^{sin(pix}) is piln(10)*10^{sin(pix)}cos(pix)
What is the first derivative of 10^{sin(pix}) ?
The first derivative of 10^{sin(pix}) is piln(10)*10^{sin(pix)}cos(pix)