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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\frac{d}{d x} ((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{\partial}{\partial y} (e^{2 x + y})

\frac{\partial}{\partial x} (\frac{x ^{2} - 2 x}{( x - 1 ) ^{2}})

\int e^{- b x} d x

\int_{1}^{3} x^{2} ln (x) d x

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

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