What is the derivative of ax+bx+ay(x+by(x)) ?

The derivative of ax+bx+ay(x+by(x)) is a+b+a derivative of {y}(x)+b derivative of {y}(x)

What is the first derivative of ax+bx+ay(x+by(x)) ?

The first derivative of ax+bx+ay(x+by(x)) is a+b+a derivative of {y}(x)+b derivative of {y}(x)

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\frac{d}{d x} (a x + b x + a y (x) + b y (x))

a + b + a \frac{d}{d x} (y (x)) + b \frac{d}{d x} (y (x))

Solution steps

\frac{d}{d x} (a x + b x + a y (x) + b y (x))

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (a x) + \frac{d}{d x} (b x) + \frac{d}{d x} (a y (x)) + \frac{d}{d x} (b y (x))

\frac{d}{d x} (a x) = a

\frac{d}{d x} (b x) = b

\frac{d}{d x} (a y (x)) = a \frac{d}{d x} (y (x))

\frac{d}{d x} (b y (x)) = b \frac{d}{d x} (y (x))

= a + b + a \frac{d}{d x} (y (x)) + b \frac{d}{d x} (y (x))

\int 3 sec^{6} (x) d x

\frac{\partial}{\partial y} (\frac{8 x}{4 x ^{2} + 5 y ^{2}})

5 x, 2 x^{2}, 0, 2.5

\int x^{2} cos^{5} (2 x) d x

\int \frac{3 x}{x ^{2} + x - 2} d x

What is the derivative of ax+bx+ay(x+by(x)) ?
The derivative of ax+bx+ay(x+by(x)) is a+b+a derivative of {y}(x)+b derivative of {y}(x)
What is the first derivative of ax+bx+ay(x+by(x)) ?
The first derivative of ax+bx+ay(x+by(x)) is a+b+a derivative of {y}(x)+b derivative of {y}(x)