What is the derivative of f(x)=(x+3)^4(7-x)^5 ?

The derivative of f(x)=(x+3)^4(7-x)^5 is 4(x+3)^3(7-x)^5-5(7-x)^4(x+3)^4

What is the first derivative of f(x)=(x+3)^4(7-x)^5 ?

The first derivative of f(x)=(x+3)^4(7-x)^5 is 4(x+3)^3(7-x)^5-5(7-x)^4(x+3)^4

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derivative of

f (x) = (x + 3)^{4} (7 - x)^{5}

4 (x + 3)^{3} (7 - x)^{5} - 5 (7 - x)^{4} (x + 3)^{4}

Solution steps

\frac{d}{d x} ((x + 3)^{4} (7 - x)^{5})

Apply the Product Rule:

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

f = (x + 3)^{4}, g = (7 - x)^{5}

= \frac{d}{d x} ((x + 3)^{4}) (7 - x)^{5} + \frac{d}{d x} ((7 - x)^{5}) (x + 3)^{4}

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

\frac{d}{d x} ((7 - x)^{5}) = - 5 (7 - x)^{4}

= 4 (x + 3)^{3} (7 - x)^{5} + (- 5 (7 - x)^{4}) (x + 3)^{4}

Simplify

= 4 (x + 3)^{3} (7 - x)^{5} - 5 (7 - x)^{4} (x + 3)^{4}

\frac{\partial}{\partial y} (x y + z)

\frac{d}{d x} (\frac{1}{( 2 x + 3 ) ^{3}})

y = x^{2} ln (7 x)

a \to \infty lim (a^{2})

\int_{1}^{6} \frac{6}{x} d x

What is the derivative of f(x)=(x+3)^4(7-x)^5 ?
The derivative of f(x)=(x+3)^4(7-x)^5 is 4(x+3)^3(7-x)^5-5(7-x)^4(x+3)^4
What is the first derivative of f(x)=(x+3)^4(7-x)^5 ?
The first derivative of f(x)=(x+3)^4(7-x)^5 is 4(x+3)^3(7-x)^5-5(7-x)^4(x+3)^4