What is the derivative of y=log_{10}(sin^2(x)) ?

The derivative of y=log_{10}(sin^2(x)) is (sin(2x))/(ln(10)sin^2(x))

What is the first derivative of y=log_{10}(sin^2(x)) ?

The first derivative of y=log_{10}(sin^2(x)) is (sin(2x))/(ln(10)sin^2(x))

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derivative of

y = lo g_{10} (sin^{2} (x))

\frac{sin ( 2 x )}{ln ( 10 ) sin ^{2} ( x )}

Solution steps

\frac{d}{d x} (lo g_{10} (sin^{2} (x)))

Apply log rule:

lo g_{a} (b) = \frac{ln ( b )}{ln ( a )}

= \frac{d}{d x} (\frac{ln ( sin ^{2} ( x ) )}{ln ( 10 )})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{ln ( 10 )} \frac{d}{d x} (ln (sin^{2} (x)))

Apply the chain rule:

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

= \frac{1}{sin ^{2} ( x )} \frac{d}{d x} (sin^{2} (x))

\frac{d}{d x} (sin^{2} (x)) = sin (2 x)

= \frac{1}{ln ( 10 )} \cdot \frac{1}{sin ^{2} ( x )} sin (2 x)

Simplify

\frac{1}{ln ( 10 )} \cdot \frac{1}{sin ^{2} ( x )} sin (2 x) : \frac{sin ( 2 x )}{ln ( 10 ) sin ^{2} ( x )}

= \frac{sin ( 2 x )}{ln ( 10 ) sin ^{2} ( x )}

What is the derivative of y=log_{10}(sin^2(x)) ?
The derivative of y=log_{10}(sin^2(x)) is (sin(2x))/(ln(10)sin^2(x))
What is the first derivative of y=log_{10}(sin^2(x)) ?
The first derivative of y=log_{10}(sin^2(x)) is (sin(2x))/(ln(10)sin^2(x))