What is the derivative of f(x)=(x+1)^3(x+4)(x-3)^2 ?

The derivative of f(x)=(x+1)^3(x+4)(x-3)^2 is 3(x+1)^2(x+4)(x-3)^2+(3x^2-4x-15)(x+1)^3

What is the first derivative of f(x)=(x+1)^3(x+4)(x-3)^2 ?

The first derivative of f(x)=(x+1)^3(x+4)(x-3)^2 is 3(x+1)^2(x+4)(x-3)^2+(3x^2-4x-15)(x+1)^3

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derivative of

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

3 (x + 1)^{2} (x + 4) (x - 3)^{2} + (3 x^{2} - 4 x - 15) (x + 1)^{3}

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = (x + 1)^{3}, g = (x + 4) (x - 3)^{2}

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

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

\frac{d}{d x} ((x + 4) (x - 3)^{2}) = 3 x^{2} - 4 x - 15

= 3 (x + 1)^{2} (x + 4) (x - 3)^{2} + (3 x^{2} - 4 x - 15) (x + 1)^{3}

x \to 3 + lim (x^{3} - c x)

f (x) = 4 x^{2} - 5 x, at x = - 1

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

\frac{d}{d t} (2 e^{t} sin (t))

What is the derivative of f(x)=(x+1)^3(x+4)(x-3)^2 ?
The derivative of f(x)=(x+1)^3(x+4)(x-3)^2 is 3(x+1)^2(x+4)(x-3)^2+(3x^2-4x-15)(x+1)^3
What is the first derivative of f(x)=(x+1)^3(x+4)(x-3)^2 ?
The first derivative of f(x)=(x+1)^3(x+4)(x-3)^2 is 3(x+1)^2(x+4)(x-3)^2+(3x^2-4x-15)(x+1)^3