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Popular >

derivative of (x^3+2(x^2+1))

Solution

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

Solution

5 x^{4} + 3 x^{2} + 4 x

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

= 3 x^{2} (x^{2} + 1) + 2 x (x^{3} + 2)

Simplify

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

= 5 x^{4} + 3 x^{2} + 4 x

Popular Examples

derivative of sin(x*x)

\frac{d}{d x} (sin (x) \cdot x)

(\partial)/(\partial {b)}(e^asin(a+{b}))

\frac{\partial}{\partial b} (e^{a} sin (a + b))

integral of sqrt(x^2-4x+40)

\int x^{2} - 4 x + 40 d x

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

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

derivative of f(x)=(12x^3-9x)^{4/3}derivative of

f (x) = (12 x^{3} - 9 x)^{\frac{4}{3}}

Frequently Asked Questions (FAQ)

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