What is the derivative of 10^{tan(2x}) ?

The derivative of 10^{tan(2x}) is ln(10)*5^{tan(2x)}*2^{tan(2x)+1}sec^2(2x)

What is the first derivative of 10^{tan(2x}) ?

The first derivative of 10^{tan(2x}) is ln(10)*5^{tan(2x)}*2^{tan(2x)+1}sec^2(2x)

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\frac{d}{d x} (1 0^{t a n (2 x)})

ln (10) \cdot 5^{t a n (2 x)} \cdot 2^{t a n (2 x) + 1} sec^{2} (2 x)

Solution steps

\frac{d}{d x} (1 0^{t a n (2 x)})

Apply exponent rule:

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

1 0^{t a n (2 x)} = e^{t a n (2 x) l n (10)}

= \frac{d}{d x} (e^{t a n (2 x) l n (10)})

Apply the chain rule:

e^{t a n (2 x) l n (10)} \frac{d}{d x} (tan (2 x) ln (10))

= e^{t a n (2 x) l n (10)} \frac{d}{d x} (tan (2 x) ln (10))

\frac{d}{d x} (tan (2 x) ln (10)) = ln (10) sec^{2} (2 x) \cdot 2

= e^{t a n (2 x) l n (10)} ln (10) sec^{2} (2 x) \cdot 2

Simplify

e^{t a n (2 x) l n (10)} ln (10) sec^{2} (2 x) \cdot 2 : ln (10) \cdot 5^{t a n (2 x)} \cdot 2^{t a n (2 x) + 1} sec^{2} (2 x)

= ln (10) \cdot 5^{t a n (2 x)} \cdot 2^{t a n (2 x) + 1} sec^{2} (2 x)

y^{^{''}} + 16 y = sin (4 x)

\int \frac{cosh ( x )}{1 + sinh ( x )} d x

\int \frac{1}{( e ^{x} + 1 )} d x

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

y^{^{'}} - \frac{4 y}{x} = - \frac{2}{x ^{2}}

What is the derivative of 10^{tan(2x}) ?
The derivative of 10^{tan(2x}) is ln(10)*5^{tan(2x)}*2^{tan(2x)+1}sec^2(2x)
What is the first derivative of 10^{tan(2x}) ?
The first derivative of 10^{tan(2x}) is ln(10)*5^{tan(2x)}*2^{tan(2x)+1}sec^2(2x)