What is the derivative of ln(3^xsec^3(4x)) ?

The derivative of ln(3^xsec^3(4x)) is ln(3)+12tan(4x)

What is the first derivative of ln(3^xsec^3(4x)) ?

The first derivative of ln(3^xsec^3(4x)) is ln(3)+12tan(4x)

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\frac{d}{d x} (ln (3^{x} sec^{3} (4 x)))

ln (3) + 12 tan (4 x)

Solution steps

\frac{d}{d x} (ln (3^{x} sec^{3} (4 x)))

Apply the chain rule:

\frac{1}{3 ^{x} sec ^{3} ( 4 x )} \frac{d}{d x} (3^{x} sec^{3} (4 x))

= \frac{1}{3 ^{x} sec ^{3} ( 4 x )} \frac{d}{d x} (3^{x} sec^{3} (4 x))

\frac{d}{d x} (3^{x} sec^{3} (4 x)) = ln (3) \cdot 3^{x} sec^{3} (4 x) + 4 \cdot 3^{1 + x} sec^{3} (4 x) tan (4 x)

= \frac{1}{3 ^{x} sec ^{3} ( 4 x )} (ln (3) \cdot 3^{x} sec^{3} (4 x) + 4 \cdot 3^{1 + x} sec^{3} (4 x) tan (4 x))

Simplify

\frac{1}{3 ^{x} sec ^{3} ( 4 x )} (ln (3) \cdot 3^{x} sec^{3} (4 x) + 4 \cdot 3^{1 + x} sec^{3} (4 x) tan (4 x)) : ln (3) + 12 tan (4 x)

= ln (3) + 12 tan (4 x)

\int_{- 2}^{5} 2 e^{x} (5 x^{2} + 3) d x

\int x 4 + x d x

f (x) = x^{3} - 3 x^{2} + 5, at x = - 1

\int_{0}^{6} 2

\int_{1}^{100} \frac{13}{x ^{3}} d x

What is the derivative of ln(3^xsec^3(4x)) ?
The derivative of ln(3^xsec^3(4x)) is ln(3)+12tan(4x)
What is the first derivative of ln(3^xsec^3(4x)) ?
The first derivative of ln(3^xsec^3(4x)) is ln(3)+12tan(4x)