What is the derivative of cos^-(log_{10}(x)) ?

The derivative of cos^-(log_{10}(x)) is (tan(log_{10}(x)))/(ln(10)xcos(log_{10)(x))}

What is the first derivative of cos^-(log_{10}(x)) ?

The first derivative of cos^-(log_{10}(x)) is (tan(log_{10}(x)))/(ln(10)xcos(log_{10)(x))}

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\frac{d}{d x} (cos^{-} (lo g_{10} (x)))

\frac{tan ( lo g _{10} ( x ) )}{ln ( 10 ) x cos ( lo g _{10} ( x ) )}

Solution steps

\frac{d}{d x} (cos^{-} (lo g_{10} (x)))

Apply exponent rule:

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

cos^{-} (lo g_{10} (x)) = e^{- l n (c o s (l o g_{10} (x)))}

= \frac{d}{d x} (e^{- l n (c o s (l o g_{10} (x)))})

Apply the chain rule:

e^{- l n (c o s (l o g_{10} (x)))} \frac{d}{d x} (- ln (cos (lo g_{10} (x))))

= e^{- l n (c o s (l o g_{10} (x)))} \frac{d}{d x} (- ln (cos (lo g_{10} (x))))

\frac{d}{d x} (- ln (cos (lo g_{10} (x)))) = \frac{tan ( lo g _{10} ( x ) )}{ln ( 10 ) x}

= e^{- l n (c o s (l o g_{10} (x)))} \frac{tan ( lo g _{10} ( x ) )}{ln ( 10 ) x}

Simplify

e^{- l n (c o s (l o g_{10} (x)))} \frac{tan ( lo g _{10} ( x ) )}{ln ( 10 ) x} : \frac{tan ( lo g _{10} ( x ) )}{ln ( 10 ) x cos ( lo g _{10} ( x ) )}

= \frac{tan ( lo g _{10} ( x ) )}{ln ( 10 ) x cos ( lo g _{10} ( x ) )}

f (x) = 2^{(x - 3)}

f (x) = \frac{2 x ^{4} + x ^{3} - 7 x ^{2} + 3}{x ^{4} + x ^{3} - x ^{2} + 2}

y = sin (2 x - \frac{π}{2}) + 2

f (t) = 9 t^{2}

f (x) = 5 x - 16

What is the derivative of cos^-(log_{10}(x)) ?
The derivative of cos^-(log_{10}(x)) is (tan(log_{10}(x)))/(ln(10)xcos(log_{10)(x))}
What is the first derivative of cos^-(log_{10}(x)) ?
The first derivative of cos^-(log_{10}(x)) is (tan(log_{10}(x)))/(ln(10)xcos(log_{10)(x))}