What is (\partial)/(\partial x)(5(y+3)(x-5)^3) ?

The answer to (\partial)/(\partial x)(5(y+3)(x-5)^3) is 15(y+3)(x-5)^2

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(\partial)/(\partial x)(5(y+3)(x-5)^3)

\frac{\partial}{\partial x} (5 (y + 3) (x - 5)^{3})

15 (y + 3) (x - 5)^{2}

Solution steps

\frac{\partial}{\partial x} (5 (y + 3) (x - 5)^{3})

Treat

y

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 5 (y + 3) \frac{\partial}{\partial x} ((x - 5)^{3})

Apply the chain rule:

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

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

\frac{\partial}{\partial x} (x - 5) = 1

= 5 (y + 3) \cdot 3 (x - 5)^{2} \cdot 1

Simplify

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

\int \frac{x ^{2}}{( x - 6 ) ( x - 7 ) ^{2}} d x

t e^{7 t}

\frac{d y}{d t} = 3 y + y^{5}, y (0) = 1

\int \frac{5.45}{( 1 + 1.9 t ) ^{0.9}} d t

\frac{d}{d x} (\frac{1}{8} ln (5 x^{2} - 2))

What is (\partial)/(\partial x)(5(y+3)(x-5)^3) ?
The answer to (\partial)/(\partial x)(5(y+3)(x-5)^3) is 15(y+3)(x-5)^2