What is the derivative of e^{ax+by(x}) ?

The derivative of e^{ax+by(x}) is e^{ax+b{y}(x)}(a+b derivative of {y}(x))

What is the first derivative of e^{ax+by(x}) ?

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

(4 x^{2} y^{4}) (2 x^{2} y^{4})

5 (53)

\frac{( 0.03 ) ^{3}}{( 0.04 ) ^{3}}

e^{- 2.303}

25.78 \cdot 1 0^{- 8}

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