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Popular >

derivative of (x^2+2)(x^3+6)

Solution

derivative of

(x^{2} + 2) (x^{3} + 6)

Solution

5 x^{4} + 6 x^{2} + 12 x

Solution steps

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

Apply the Product Rule:

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

f = x^{2} + 2, g = x^{3} + 6

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

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

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

= 2 x (x^{3} + 6) + 3 x^{2} (x^{2} + 2)

Simplify

2 x (x^{3} + 6) + 3 x^{2} (x^{2} + 2) : 5 x^{4} + 6 x^{2} + 12 x

= 5 x^{4} + 6 x^{2} + 12 x

Popular Examples

integral of cos(x)e^{-sx}

\int cos (x) e^{- s x} d x

(\partial)/(\partial x)(x^2+1+z^3)

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

slope of (5/8 ,-2),(-1/4 ,-1/4)slope

(\frac{5}{8}, - 2), (- \frac{1}{4}, - \frac{1}{4})

tangent of y^2-xy-10=0,(-3,-5)tangent of

y^{2} - x y - 10 = 0, (- 3, - 5)

y^{''}+6y=-294x^2e^{6x}

y^{^{''}} + 6 y = - 294 x^{2} e^{6 x}

Frequently Asked Questions (FAQ)

What is the derivative of (x^2+2)(x^3+6) ?
The derivative of (x^2+2)(x^3+6) is 5x^4+6x^2+12x
What is the first derivative of (x^2+2)(x^3+6) ?
The first derivative of (x^2+2)(x^3+6) is 5x^4+6x^2+12x