derivative of a+b^1x^1+b^2x^2

Lösung

\frac{d}{d x} (a + b^{1} x^{1} + b^{2} x^{2})

2 b^{2} x + b

Schritte zur Lösung

\frac{d}{d x} (a + b^{1} x^{1} + b^{2} x^{2})

Vereinfache

a + b^{1} x^{1} + b^{2} x^{2} : a + b x + b^{2} x^{2}

= \frac{d}{d x} (a + b x + b^{2} x^{2})

Wende die Summen-/Differenzregel an:

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

= \frac{d a}{d x} + \frac{d}{d x} (b x) + \frac{d}{d x} (b^{2} x^{2})

\frac{d a}{d x} = 0

\frac{d}{d x} (b x) = b

\frac{d}{d x} (b^{2} x^{2}) = 2 b^{2} x

= 0 + b + 2 b^{2} x

Vereinfache

= 2 b^{2} x + b

d er i v a t i v e \frac{( x ^{2} + 2 ) ^{3}}{2}

\frac{d}{d t} (3 cos^{6} (t))

d er i v a t i v e f (x) = \frac{( x ^{3} + 4 x - 1 )}{x ^{2}}

d er i v a t i v e \frac{( 1 + 2 x + x ^{2} )}{e ^{x}}

d er i v a t i v e \frac{x ^{2}}{2 + 3 x}