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

The derivative of f(x)=(x^3-4)^2(2x+5)^3 is 6x^2(x^3-4)(2x+5)^3+6(2x+5)^2(x^3-4)^2

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

The first derivative of f(x)=(x^3-4)^2(2x+5)^3 is 6x^2(x^3-4)(2x+5)^3+6(2x+5)^2(x^3-4)^2

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derivative of

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d}{d x} ((x^{3} - 4)^{2}) = 6 x^{2} (x^{3} - 4)

\frac{d}{d x} ((2 x + 5)^{3}) = 6 (2 x + 5)^{2}

= 6 x^{2} (x^{3} - 4) (2 x + 5)^{3} + 6 (2 x + 5)^{2} (x^{3} - 4)^{2}

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

\int \frac{6 x ^{2} + 5 x + 6}{( x ^{2} + 1 ) ^{2}} d x

y^{^{'}} = \frac{3 ^{2} y ^{2} + 1}{3}, y (0) = - 0.5

\int_{0}^{5} π (25 - y^{2}) d y

\frac{\partial}{\partial x} (ln (x + 3 y + 5 z))

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