derivative of sin(tan(sqrt(1+x^3)))

Lösung

\frac{d}{d x} (sin (tan (1 + x^{3})))

\frac{3 x ^{2} sec ^{2} ( 1 + x ^{3} ) cos ( tan ( 1 + x ^{3} ) )}{2 1 + x ^{3}}

Schritte zur Lösung

\frac{d}{d x} (sin (tan (1 + x^{3})))

Wende die Kettenregel an:

cos (tan (1 + x^{3})) \frac{d}{d x} (tan (1 + x^{3}))

= cos (tan (1 + x^{3})) \frac{d}{d x} (tan (1 + x^{3}))

\frac{d}{d x} (tan (1 + x^{3})) = \frac{3 x ^{2} sec ^{2} ( 1 + x ^{3} )}{2 1 + x ^{3}}

= cos (tan (1 + x^{3})) \frac{3 x ^{2} sec ^{2} ( 1 + x ^{3} )}{2 1 + x ^{3}}

Multipliziere Brüche:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{3 x ^{2} sec ^{2} ( 1 + x ^{3} ) cos ( tan ( 1 + x ^{3} ) )}{2 1 + x ^{3}}

\frac{d x}{d y} = 1 + x^{2}

\int \frac{e ^{- x}}{1 - e ^{- x}} d x

\frac{\partial}{\partial x} (x^{3} y^{4} sin^{2} (x y))

\int \frac{1}{( t ^{2} + 1 ) ^{2}} d t

\int \frac{x}{x - 2} d x