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

The derivative of f(x)=(x(x^5+9)^3) is (x^5+9)^3+15x^5(x^5+9)^2

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

The first derivative of f(x)=(x(x^5+9)^3) is (x^5+9)^3+15x^5(x^5+9)^2

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derivative of

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

(x^{5} + 9)^{3} + 15 x^{5} (x^{5} + 9)^{2}

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d x}{d x} = 1

\frac{d}{d x} ((x^{5} + 9)^{3}) = 15 x^{4} (x^{5} + 9)^{2}

= 1 \cdot (x^{5} + 9)^{3} + 15 x^{4} (x^{5} + 9)^{2} x

Simplify

1 \cdot (x^{5} + 9)^{3} + 15 x^{4} (x^{5} + 9)^{2} x : (x^{5} + 9)^{3} + 15 x^{5} (x^{5} + 9)^{2}

= (x^{5} + 9)^{3} + 15 x^{5} (x^{5} + 9)^{2}

\int e^{4 θ} sin (5 θ) d θ

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

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What is the derivative of f(x)=(x(x^5+9)^3) ?
The derivative of f(x)=(x(x^5+9)^3) is (x^5+9)^3+15x^5(x^5+9)^2
What is the first derivative of f(x)=(x(x^5+9)^3) ?
The first derivative of f(x)=(x(x^5+9)^3) is (x^5+9)^3+15x^5(x^5+9)^2