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

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

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

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

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derivative of

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

x^{2} - 3 x, 3 x + 7

x \to - 4 lim ((x - 4)^{2} + 2)

9 x^{3} + 7^{x} + 20

\int \frac{u}{( u - 1 ) ^{2}} d u

\int \frac{x ^{4}}{x ^{5} - 1} d x

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