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

The derivative of (3x^2-x^2(2x+5)) is 2(6x^2+10x)

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

The first derivative of (3x^2-x^2(2x+5)) is 2(6x^2+10x)

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

2 (6 x^{2} + 10 x)

Solution steps

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

Simplify

(3 x^{2} - x^{2}) (2 x + 5) : 2 x^{2} (2 x + 5)

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Product Rule:

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

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

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

\frac{d}{d x} (x^{2}) = 2 x

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

= 2 (2 x (2 x + 5) + 2 x^{2})

Expand

2 x (2 x + 5) + 2 x^{2} : 6 x^{2} + 10 x

= 2 (6 x^{2} + 10 x)

\int \frac{1 - 2 x}{x} d x

y (1 + x^{2}) y^{^{'}} - x (2 + y^{2}) = 0, y (0) = 3

\int \frac{x ^{2}}{( 4 - x ^{3} ) ^{2}} d x

f (x) = sin (arccos (x))

\frac{3600}{x}

What is the derivative of (3x^2-x^2(2x+5)) ?
The derivative of (3x^2-x^2(2x+5)) is 2(6x^2+10x)
What is the first derivative of (3x^2-x^2(2x+5)) ?
The first derivative of (3x^2-x^2(2x+5)) is 2(6x^2+10x)