What is the derivative of 3^{tan(x}) ?

The derivative of 3^{tan(x}) is ln(3)*3^{tan(x)}sec^2(x)

What is the first derivative of 3^{tan(x}) ?

The first derivative of 3^{tan(x}) is ln(3)*3^{tan(x)}sec^2(x)

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\frac{d}{d x} (3^{t a n (x)})

ln (3) \cdot 3^{t a n (x)} sec^{2} (x)

Solution steps

\frac{d}{d x} (3^{t a n (x)})

Apply exponent rule:

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

3^{t a n (x)} = e^{t a n (x) l n (3)}

= \frac{d}{d x} (e^{t a n (x) l n (3)})

Apply the chain rule:

e^{t a n (x) l n (3)} \frac{d}{d x} (tan (x) ln (3))

= e^{t a n (x) l n (3)} \frac{d}{d x} (tan (x) ln (3))

\frac{d}{d x} (tan (x) ln (3)) = ln (3) sec^{2} (x)

= e^{t a n (x) l n (3)} ln (3) sec^{2} (x)

e^{t a n (x) l n (3)} = 3^{t a n (x)}

= ln (3) \cdot 3^{t a n (x)} sec^{2} (x)

What is the derivative of 3^{tan(x}) ?
The derivative of 3^{tan(x}) is ln(3)*3^{tan(x)}sec^2(x)
What is the first derivative of 3^{tan(x}) ?
The first derivative of 3^{tan(x}) is ln(3)*3^{tan(x)}sec^2(x)