What is the derivative of f(x)=(3x^3+5)(x^4-5x) ?

The derivative of f(x)=(3x^3+5)(x^4-5x) is 21x^6-40x^3-25

What is the first derivative of f(x)=(3x^3+5)(x^4-5x) ?

The first derivative of f(x)=(3x^3+5)(x^4-5x) is 21x^6-40x^3-25

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derivative of

f (x) = (3 x^{3} + 5) (x^{4} - 5 x)

21 x^{6} - 40 x^{3} - 25

Solution steps

\frac{d}{d x} ((3 x^{3} + 5) (x^{4} - 5 x))

Apply the Product Rule:

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

f = 3 x^{3} + 5, g = x^{4} - 5 x

= \frac{d}{d x} (3 x^{3} + 5) (x^{4} - 5 x) + \frac{d}{d x} (x^{4} - 5 x) (3 x^{3} + 5)

\frac{d}{d x} (3 x^{3} + 5) = 9 x^{2}

\frac{d}{d x} (x^{4} - 5 x) = 4 x^{3} - 5

= 9 x^{2} (x^{4} - 5 x) + (4 x^{3} - 5) (3 x^{3} + 5)

Simplify

9 x^{2} (x^{4} - 5 x) + (4 x^{3} - 5) (3 x^{3} + 5) : 21 x^{6} - 40 x^{3} - 25

= 21 x^{6} - 40 x^{3} - 25

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

2 y^{^{'}} = y

\frac{\partial}{\partial x} (4 sin^{2} (x))

f (x) = \frac{2}{x}

e^{π}

What is the derivative of f(x)=(3x^3+5)(x^4-5x) ?
The derivative of f(x)=(3x^3+5)(x^4-5x) is 21x^6-40x^3-25
What is the first derivative of f(x)=(3x^3+5)(x^4-5x) ?
The first derivative of f(x)=(3x^3+5)(x^4-5x) is 21x^6-40x^3-25