What is the derivative of f(x)=(2x^3+3x)(x-3)(x+5) ?

The derivative of f(x)=(2x^3+3x)(x-3)(x+5) is 10x^4+16x^3-81x^2+12x-45

What is the first derivative of f(x)=(2x^3+3x)(x-3)(x+5) ?

The first derivative of f(x)=(2x^3+3x)(x-3)(x+5) is 10x^4+16x^3-81x^2+12x-45

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derivative of

f (x) = (2 x^{3} + 3 x) (x - 3) (x + 5)

10 x^{4} + 16 x^{3} - 81 x^{2} + 12 x - 45

Solution steps

\frac{d}{d x} ((2 x^{3} + 3 x) (x - 3) (x + 5))

Apply the Product Rule:

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

f = 2 x^{3} + 3 x, g = (x - 3) (x + 5)

= \frac{d}{d x} (2 x^{3} + 3 x) (x - 3) (x + 5) + \frac{d}{d x} ((x - 3) (x + 5)) (2 x^{3} + 3 x)

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

\frac{d}{d x} ((x - 3) (x + 5)) = 2 x + 2

= (6 x^{2} + 3) (x - 3) (x + 5) + (2 x + 2) (2 x^{3} + 3 x)

Simplify

(6 x^{2} + 3) (x - 3) (x + 5) + (2 x + 2) (2 x^{3} + 3 x) : 10 x^{4} + 16 x^{3} - 81 x^{2} + 12 x - 45

= 10 x^{4} + 16 x^{3} - 81 x^{2} + 12 x - 45

y^{^{''}} - 8 y^{^{'}} + 20 y = 100 x^{2} - 26 x e^{x}

\int - x + 2 d x

\frac{d}{d x} (16 ln (x))

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

y^{^{''}} - 3 y^{^{'}} + 2 y = 14 sin (2 x) - 18 cos (2 x)

What is the derivative of f(x)=(2x^3+3x)(x-3)(x+5) ?
The derivative of f(x)=(2x^3+3x)(x-3)(x+5) is 10x^4+16x^3-81x^2+12x-45
What is the first derivative of f(x)=(2x^3+3x)(x-3)(x+5) ?
The first derivative of f(x)=(2x^3+3x)(x-3)(x+5) is 10x^4+16x^3-81x^2+12x-45