What is the derivative of sin(3xln(sech(2x))) ?

The derivative of sin(3xln(sech(2x))) is 3cos(3x)ln(sech(2x))-2tanh(2x)sin(3x)

What is the first derivative of sin(3xln(sech(2x))) ?

The first derivative of sin(3xln(sech(2x))) is 3cos(3x)ln(sech(2x))-2tanh(2x)sin(3x)

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\frac{d}{d x} (sin (3 x) ln (sech (2 x)))

3 cos (3 x) ln (sech (2 x)) - 2 tanh (2 x) sin (3 x)

Solution steps

\frac{d}{d x} (sin (3 x) ln (sech (2 x)))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = sin (3 x), g = ln (sech (2 x))

= \frac{d}{d x} (sin (3 x)) ln (sech (2 x)) + \frac{d}{d x} (ln (sech (2 x))) sin (3 x)

\frac{d}{d x} (sin (3 x)) = cos (3 x) \cdot 3

\frac{d}{d x} (ln (sech (2 x))) = - 2 tanh (2 x)

= cos (3 x) \cdot 3 ln (sech (2 x)) + (- 2 tanh (2 x)) sin (3 x)

Simplify

= 3 cos (3 x) ln (sech (2 x)) - 2 tanh (2 x) sin (3 x)

\frac{\partial}{\partial y} (ln (x^{2} + y^{2} + 2))

n = 1 \sum \infty \frac{x ^{n}}{1 ^{n}}

\int (1 + x)^{3} d x

f (x) = \frac{x ^{2} - 3 x + 4}{x + 2}

1 + x - x^{2} - x^{3}, 1 - x

What is the derivative of sin(3xln(sech(2x))) ?
The derivative of sin(3xln(sech(2x))) is 3cos(3x)ln(sech(2x))-2tanh(2x)sin(3x)
What is the first derivative of sin(3xln(sech(2x))) ?
The first derivative of sin(3xln(sech(2x))) is 3cos(3x)ln(sech(2x))-2tanh(2x)sin(3x)