What is the derivative of e^{(x+y^2}) ?

The derivative of e^{(x+y^2}) is e^{(x+y)^2}*2(x+y)(1+(dy)/(dx))

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

The first derivative of e^{(x+y^2}) is e^{(x+y)^2}*2(x+y)(1+(dy)/(dx))

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

e^{(x + y)^{2}} \cdot 2 (x + y) (1 + \frac{d y}{d x})

Solution steps

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

Apply the chain rule:

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

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

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

= e^{(x + y)^{2}} \cdot 2 (x + y) (1 + \frac{d y}{d x})

x \to 4 + lim (- 3)

f (x) = \frac{2 x}{x ^{2} + 1}, 1, at x = 1

\frac{d}{d x} (cos^{2} (9 x) + sin^{2} (9 x))

\frac{d}{d t} (4 e^{t})

What is the derivative of e^{(x+y^2}) ?
The derivative of e^{(x+y^2}) is e^{(x+y)^2}*2(x+y)(1+(dy)/(dx))
What is the first derivative of e^{(x+y^2}) ?
The first derivative of e^{(x+y^2}) is e^{(x+y)^2}*2(x+y)(1+(dy)/(dx))