What is the derivative of 2^{tan(4x}) ?

The derivative of 2^{tan(4x}) is ln(2)*2^{tan(4x)+2}sec^2(4x)

What is the first derivative of 2^{tan(4x}) ?

The first derivative of 2^{tan(4x}) is ln(2)*2^{tan(4x)+2}sec^2(4x)

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\frac{d}{d x} (2^{t a n (4 x)})

ln (2) \cdot 2^{t a n (4 x) + 2} sec^{2} (4 x)

Solution steps

\frac{d}{d x} (2^{t a n (4 x)})

Apply exponent rule:

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

2^{t a n (4 x)} = e^{t a n (4 x) l n (2)}

= \frac{d}{d x} (e^{t a n (4 x) l n (2)})

Apply the chain rule:

e^{t a n (4 x) l n (2)} \frac{d}{d x} (tan (4 x) ln (2))

= e^{t a n (4 x) l n (2)} \frac{d}{d x} (tan (4 x) ln (2))

\frac{d}{d x} (tan (4 x) ln (2)) = ln (2) sec^{2} (4 x) \cdot 4

= e^{t a n (4 x) l n (2)} ln (2) sec^{2} (4 x) \cdot 4

Simplify

e^{t a n (4 x) l n (2)} ln (2) sec^{2} (4 x) \cdot 4 : ln (2) \cdot 2^{t a n (4 x) + 2} sec^{2} (4 x)

= ln (2) \cdot 2^{t a n (4 x) + 2} sec^{2} (4 x)

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\frac{d}{d x} (- \frac{x}{( 1 - x ^{2} ) ^{\frac{3}{2}}})

f (x) = x^{2} - 1, (- 1, 0)

\int_{0}^{π} 8 cos^{4} (x) sin (x) d x

\int 3 x^{2} + 1 d x

What is the derivative of 2^{tan(4x}) ?
The derivative of 2^{tan(4x}) is ln(2)*2^{tan(4x)+2}sec^2(4x)
What is the first derivative of 2^{tan(4x}) ?
The first derivative of 2^{tan(4x}) is ln(2)*2^{tan(4x)+2}sec^2(4x)