What is the derivative of by(x^2) ?

The derivative of by(x^2) is b(derivative of {y}(x)x^2+2x{y}(x))

What is the first derivative of by(x^2) ?

The first derivative of by(x^2) is b(derivative of {y}(x)x^2+2x{y}(x))

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\frac{d}{d x} (b y (x) (x)^{2})

b (\frac{d}{d x} (y (x)) x^{2} + 2 x y (x))

Solution steps

\frac{d}{d x} (b y (x) (x)^{2})

Take the constant out:

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

= b \frac{d}{d x} (y (x) x^{2})

Apply the Product Rule:

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

f = y (x), g = x^{2}

= b (\frac{d}{d x} (y (x)) x^{2} + \frac{d}{d x} (x^{2}) y (x))

\frac{d}{d x} (x^{2}) = 2 x

= b (\frac{d}{d x} (y (x)) x^{2} + 2 x y (x))

What is the derivative of by(x^2) ?
The derivative of by(x^2) is b(derivative of {y}(x)x^2+2x{y}(x))
What is the first derivative of by(x^2) ?
The first derivative of by(x^2) is b(derivative of {y}(x)x^2+2x{y}(x))