derivative of mx^{m+5}+6x^my^n+nx^{n+3}

Lösung

\frac{d}{d x} (m x^{m + 5} + 6 x^{m} y^{n} + n x^{n + 3})

m x^{m + 4} (m + 5) + 6 (m x^{m - 1} y^{n} + n y^{n - 1} \frac{d y}{d x} x^{m}) + n x^{n + 2} (n + 3)

Schritte zur Lösung

\frac{d}{d x} (m x^{m + 5} + 6 x^{m} y^{n} + n x^{n + 3})

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (m x^{m + 5}) + \frac{d}{d x} (6 x^{m} y^{n}) + \frac{d}{d x} (n x^{n + 3})

\frac{d}{d x} (m x^{m + 5}) = m x^{m + 4} (m + 5)

\frac{d}{d x} (6 x^{m} y^{n}) = 6 (m x^{m - 1} y^{n} + n y^{n - 1} \frac{d y}{d x} x^{m})

\frac{d}{d x} (n x^{n + 3}) = n x^{n + 2} (n + 3)

= m x^{m + 4} (m + 5) + 6 (m x^{m - 1} y^{n} + n y^{n - 1} \frac{d y}{d x} x^{m}) + n x^{n + 2} (n + 3)

\int ln (x) (x^{2}) d x

\int sec (2 θ) d θ

t an g e n t f (x) = 4 x^{2} - 2 x + 5

(sec^{2} (x))^{^{'}}

\int (- 4 x^{3}) d x