What is the derivative of 2+3(x-1+3(x-1)^2+d(x-1)^3) ?

The derivative of 2+3(x-1+3(x-1)^2+d(x-1)^3) is 3x^2d+6x-6xd+3d-3

What is the first derivative of 2+3(x-1+3(x-1)^2+d(x-1)^3) ?

The first derivative of 2+3(x-1+3(x-1)^2+d(x-1)^3) is 3x^2d+6x-6xd+3d-3

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\frac{d}{d x} (2 + 3 (x - 1) + 3 (x - 1)^{2} + d (x - 1)^{3})

3 x^{2} d + 6 x - 6 x d + 3 d - 3

Solution steps

\frac{d}{d x} (2 + 3 (x - 1) + 3 (x - 1)^{2} + d (x - 1)^{3})

Simplify

2 + 3 (x - 1) + 3 (x - 1)^{2} + d (x - 1)^{3} : x^{3} d + 3 x^{2} - 3 x^{2} d + 3 x d - 3 x + 2 - d

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

Treat

d

as a constant

Apply the Sum/Difference Rule:

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

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

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

\frac{d}{d x} (3 x^{2}) = 6 x

\frac{d}{d x} (3 x^{2} d) = 6 d x

\frac{d}{d x} (3 x d) = 3 d

\frac{d}{d x} (3 x) = 3

\frac{d}{d x} (2) = 0

\frac{dd}{d x} = 0

= 3 d x^{2} + 6 x - 6 d x + 3 d - 3 + 0 - 0

Simplify

= 3 x^{2} d + 6 x - 6 x d + 3 d - 3

What is the derivative of 2+3(x-1+3(x-1)^2+d(x-1)^3) ?
The derivative of 2+3(x-1+3(x-1)^2+d(x-1)^3) is 3x^2d+6x-6xd+3d-3
What is the first derivative of 2+3(x-1+3(x-1)^2+d(x-1)^3) ?
The first derivative of 2+3(x-1+3(x-1)^2+d(x-1)^3) is 3x^2d+6x-6xd+3d-3