derivative of ln(3^xsec^3(4x))

解答

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

ln (3) + 12 tan (4 x)

求解步骤

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

使用连锁律:

\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))

化简

\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

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