What is the derivative of (x^4+3x^2)(1-5x) ?

The derivative of (x^4+3x^2)(1-5x) is -25x^4+4x^3-45x^2+6x

What is the first derivative of (x^4+3x^2)(1-5x) ?

The first derivative of (x^4+3x^2)(1-5x) is -25x^4+4x^3-45x^2+6x

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derivative of

(x^{4} + 3 x^{2}) (1 - 5 x)

- 25 x^{4} + 4 x^{3} - 45 x^{2} + 6 x

Solution steps

\frac{d}{d x} ((x^{4} + 3 x^{2}) (1 - 5 x))

Apply the Product Rule:

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

f = x^{4} + 3 x^{2}, g = 1 - 5 x

= \frac{d}{d x} (x^{4} + 3 x^{2}) (1 - 5 x) + \frac{d}{d x} (1 - 5 x) (x^{4} + 3 x^{2})

\frac{d}{d x} (x^{4} + 3 x^{2}) = 4 x^{3} + 6 x

\frac{d}{d x} (1 - 5 x) = - 5

= (4 x^{3} + 6 x) (1 - 5 x) + (- 5) (x^{4} + 3 x^{2})

Simplify

(4 x^{3} + 6 x) (1 - 5 x) + (- 5) (x^{4} + 3 x^{2}) : - 25 x^{4} + 4 x^{3} - 45 x^{2} + 6 x

= - 25 x^{4} + 4 x^{3} - 45 x^{2} + 6 x

\frac{d}{d x} (2 x + 1)

f (x) = \frac{cos ( x )}{x ^{7}}

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

\frac{d y}{d x} - 3 y = \frac{y}{x}

\frac{d}{d x} ((x - y)^{10})

What is the derivative of (x^4+3x^2)(1-5x) ?
The derivative of (x^4+3x^2)(1-5x) is -25x^4+4x^3-45x^2+6x
What is the first derivative of (x^4+3x^2)(1-5x) ?
The first derivative of (x^4+3x^2)(1-5x) is -25x^4+4x^3-45x^2+6x