derivative of tan^4(cot(3x^4+5x))

Lösung

\frac{d}{d x} (tan^{4} (cot (3 x^{4} + 5 x)))

- 4 tan^{3} (cot (3 x^{4} + 5 x)) sec^{2} (cot (3 x^{4} + 5 x)) csc^{2} (3 x^{4} + 5 x) (12 x^{3} + 5)

Schritte zur Lösung

\frac{d}{d x} (tan^{4} (cot (3 x^{4} + 5 x)))

Wende die Kettenregel an:

4 (tan (cot (3 x^{4} + 5 x)))^{3} \frac{d}{d x} (tan (cot (3 x^{4} + 5 x)))

= 4 (tan (cot (3 x^{4} + 5 x)))^{3} \frac{d}{d x} (tan (cot (3 x^{4} + 5 x)))

\frac{d}{d x} (tan (cot (3 x^{4} + 5 x))) = - sec^{2} (cot (3 x^{4} + 5 x)) csc^{2} (3 x^{4} + 5 x) (12 x^{3} + 5)

= 4 (tan (cot (3 x^{4} + 5 x)))^{3} (- sec^{2} (cot (3 x^{4} + 5 x)) csc^{2} (3 x^{4} + 5 x) (12 x^{3} + 5))

Vereinfache

= - 4 tan^{3} (cot (3 x^{4} + 5 x)) sec^{2} (cot (3 x^{4} + 5 x)) csc^{2} (3 x^{4} + 5 x) (12 x^{3} + 5)

x \frac{d y}{d x} = x^{3} + 24 x^{3} y

\int (2 cos (x)) d x

\frac{d y}{d x} = \frac{3 sec ( y )}{( x - 3 ) ^{2}}

\frac{\partial}{\partial x} (5 x^{2} y^{5})

s l o p e - 2 x^{2} + 50 x + 25.247