What is the derivative of a+b^1x^1+b^2x^2 ?

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

What is the first derivative of a+b^1x^1+b^2x^2 ?

The first derivative of a+b^1x^1+b^2x^2 is 2b^2x+b

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

2 b^{2} x + b

Solution steps

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

Simplify

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})

Apply the Sum/Difference Rule:

(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

Simplify

= 2 b^{2} x + b

\frac{( x ^{2} + 2 ) ^{3}}{2}

\frac{- 2 x}{cos ( x )}

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

e^{3} x + 2

f (x) = \frac{( x ^{3} + 4 x - 1 )}{x ^{2}}

What is the derivative of a+b^1x^1+b^2x^2 ?
The derivative of a+b^1x^1+b^2x^2 is 2b^2x+b
What is the first derivative of a+b^1x^1+b^2x^2 ?
The first derivative of a+b^1x^1+b^2x^2 is 2b^2x+b