What is the derivative of 3ax^4-4ax^3-5bx^2+7cx ?

The derivative of 3ax^4-4ax^3-5bx^2+7cx is 12ax^3-12ax^2-10bx+7c

What is the first derivative of 3ax^4-4ax^3-5bx^2+7cx ?

The first derivative of 3ax^4-4ax^3-5bx^2+7cx is 12ax^3-12ax^2-10bx+7c

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\frac{d}{d x} (3 a x^{4} - 4 a x^{3} - 5 b x^{2} + 7 c x)

12 a x^{3} - 12 a x^{2} - 10 b x + 7 c

Solution steps

\frac{d}{d x} (3 a x^{4} - 4 a x^{3} - 5 b x^{2} + 7 c x)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (3 a x^{4}) - \frac{d}{d x} (4 a x^{3}) - \frac{d}{d x} (5 b x^{2}) + \frac{d}{d x} (7 c x)

\frac{d}{d x} (3 a x^{4}) = 12 a x^{3}

\frac{d}{d x} (4 a x^{3}) = 12 a x^{2}

\frac{d}{d x} (5 b x^{2}) = 10 b x

\frac{d}{d x} (7 c x) = 7 c

= 12 a x^{3} - 12 a x^{2} - 10 b x + 7 c

What is the derivative of 3ax^4-4ax^3-5bx^2+7cx ?
The derivative of 3ax^4-4ax^3-5bx^2+7cx is 12ax^3-12ax^2-10bx+7c
What is the first derivative of 3ax^4-4ax^3-5bx^2+7cx ?
The first derivative of 3ax^4-4ax^3-5bx^2+7cx is 12ax^3-12ax^2-10bx+7c