What is the derivative of (x^2+9)(x^3+5) ?

The derivative of (x^2+9)(x^3+5) is 5x^4+27x^2+10x

What is the first derivative of (x^2+9)(x^3+5) ?

The first derivative of (x^2+9)(x^3+5) is 5x^4+27x^2+10x

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derivative of

(x^{2} + 9) (x^{3} + 5)

5 x^{4} + 27 x^{2} + 10 x

Solution steps

\frac{d}{d x} ((x^{2} + 9) (x^{3} + 5))

Apply the Product Rule:

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

f = x^{2} + 9, g = x^{3} + 5

= \frac{d}{d x} (x^{2} + 9) (x^{3} + 5) + \frac{d}{d x} (x^{3} + 5) (x^{2} + 9)

\frac{d}{d x} (x^{2} + 9) = 2 x

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

= 2 x (x^{3} + 5) + 3 x^{2} (x^{2} + 9)

Simplify

2 x (x^{3} + 5) + 3 x^{2} (x^{2} + 9) : 5 x^{4} + 27 x^{2} + 10 x

= 5 x^{4} + 27 x^{2} + 10 x

\frac{( x ^{4} + 9 )}{x ^{2}}

tan^{- 2} (x)

2 t + 5

\frac{d}{d a} (\frac{( a - t ^{2} )}{( b \cdot x )})

- 12 x

What is the derivative of (x^2+9)(x^3+5) ?
The derivative of (x^2+9)(x^3+5) is 5x^4+27x^2+10x
What is the first derivative of (x^2+9)(x^3+5) ?
The first derivative of (x^2+9)(x^3+5) is 5x^4+27x^2+10x