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

The derivative of (x^2+3)^4(x^2+5)^2 is 8x(x^2+3)^3(x^2+5)^2+4x(x^2+5)(x^2+3)^4

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

The first derivative of (x^2+3)^4(x^2+5)^2 is 8x(x^2+3)^3(x^2+5)^2+4x(x^2+5)(x^2+3)^4

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derivative of

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

8 x (x^{2} + 3)^{3} (x^{2} + 5)^{2} + 4 x (x^{2} + 5) (x^{2} + 3)^{4}

Solution steps

\frac{d}{d x} ((x^{2} + 3)^{4} (x^{2} + 5)^{2})

Apply the Product Rule:

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

f = (x^{2} + 3)^{4}, g = (x^{2} + 5)^{2}

= \frac{d}{d x} ((x^{2} + 3)^{4}) (x^{2} + 5)^{2} + \frac{d}{d x} ((x^{2} + 5)^{2}) (x^{2} + 3)^{4}

\frac{d}{d x} ((x^{2} + 3)^{4}) = 8 x (x^{2} + 3)^{3}

\frac{d}{d x} ((x^{2} + 5)^{2}) = 4 x (x^{2} + 5)

= 8 x (x^{2} + 3)^{3} (x^{2} + 5)^{2} + 4 x (x^{2} + 5) (x^{2} + 3)^{4}

\frac{d}{d t} (50 + 4 t)

(e^{9 x})^{2}

e^{x} y^{2}

3 - 2 x + 4 x^{2}

2 x^{\frac{- 1}{2}}

What is the derivative of (x^2+3)^4(x^2+5)^2 ?
The derivative of (x^2+3)^4(x^2+5)^2 is 8x(x^2+3)^3(x^2+5)^2+4x(x^2+5)(x^2+3)^4
What is the first derivative of (x^2+3)^4(x^2+5)^2 ?
The first derivative of (x^2+3)^4(x^2+5)^2 is 8x(x^2+3)^3(x^2+5)^2+4x(x^2+5)(x^2+3)^4