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

The derivative of f(x)=(x^3-5x)(5x^2+3x) is 25x^4+12x^3-75x^2-30x

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

The first derivative of f(x)=(x^3-5x)(5x^2+3x) is 25x^4+12x^3-75x^2-30x

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derivative of

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

25 x^{4} + 12 x^{3} - 75 x^{2} - 30 x

Solution steps

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

Apply the Product Rule:

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

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

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

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

\frac{d}{d x} (5 x^{2} + 3 x) = 10 x + 3

= (3 x^{2} - 5) (5 x^{2} + 3 x) + (10 x + 3) (x^{3} - 5 x)

Simplify

(3 x^{2} - 5) (5 x^{2} + 3 x) + (10 x + 3) (x^{3} - 5 x) : 25 x^{4} + 12 x^{3} - 75 x^{2} - 30 x

= 25 x^{4} + 12 x^{3} - 75 x^{2} - 30 x

\frac{\partial}{\partial x} ([A x^{2} + B y^{3}]^{\frac{1}{4}})

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\int_{0}^{5} π (2 7 y)^{2} d y

\int_{2}^{\infty} e^{- 9 x} d x

What is the derivative of f(x)=(x^3-5x)(5x^2+3x) ?
The derivative of f(x)=(x^3-5x)(5x^2+3x) is 25x^4+12x^3-75x^2-30x
What is the first derivative of f(x)=(x^3-5x)(5x^2+3x) ?
The first derivative of f(x)=(x^3-5x)(5x^2+3x) is 25x^4+12x^3-75x^2-30x