What is the derivative of f(x)=(2x+3)^{11}(4-5x)^9 ?

The derivative of f(x)=(2x+3)^{11}(4-5x)^9 is 22(2x+3)^{10}(4-5x)^9-45(4-5x)^8(2x+3)^{11}

What is the first derivative of f(x)=(2x+3)^{11}(4-5x)^9 ?

The first derivative of f(x)=(2x+3)^{11}(4-5x)^9 is 22(2x+3)^{10}(4-5x)^9-45(4-5x)^8(2x+3)^{11}

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derivative of

f (x) = (2 x + 3)^{11} (4 - 5 x)^{9}

22 (2 x + 3)^{10} (4 - 5 x)^{9} - 45 (4 - 5 x)^{8} (2 x + 3)^{11}

Solution steps

\frac{d}{d x} ((2 x + 3)^{11} (4 - 5 x)^{9})

Apply the Product Rule:

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

f = (2 x + 3)^{11}, g = (4 - 5 x)^{9}

= \frac{d}{d x} ((2 x + 3)^{11}) (4 - 5 x)^{9} + \frac{d}{d x} ((4 - 5 x)^{9}) (2 x + 3)^{11}

\frac{d}{d x} ((2 x + 3)^{11}) = 22 (2 x + 3)^{10}

\frac{d}{d x} ((4 - 5 x)^{9}) = - 45 (4 - 5 x)^{8}

= 22 (2 x + 3)^{10} (4 - 5 x)^{9} + (- 45 (4 - 5 x)^{8}) (2 x + 3)^{11}

Simplify

= 22 (2 x + 3)^{10} (4 - 5 x)^{9} - 45 (4 - 5 x)^{8} (2 x + 3)^{11}

x \to 1 + lim (1)

\frac{9}{10} x^{2} d y - 18 d x = 0

\frac{\partial}{\partial x} (x^{3} + x^{2} y - y^{2} - 4 y)

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

x \to 5 + lim (\frac{2}{x + 5})

What is the derivative of f(x)=(2x+3)^{11}(4-5x)^9 ?
The derivative of f(x)=(2x+3)^{11}(4-5x)^9 is 22(2x+3)^{10}(4-5x)^9-45(4-5x)^8(2x+3)^{11}
What is the first derivative of f(x)=(2x+3)^{11}(4-5x)^9 ?
The first derivative of f(x)=(2x+3)^{11}(4-5x)^9 is 22(2x+3)^{10}(4-5x)^9-45(4-5x)^8(2x+3)^{11}