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Popular >

derivative of e^{sin(x+y})

Solution

\frac{d}{d x} (e^{s i n (x + y)})

Solution

e^{s i n (x + y)} cos (x + y) (1 + \frac{d y}{d x})

Solution steps

\frac{d}{d x} (e^{s i n (x + y)})

Apply the chain rule:

e^{s i n (x + y)} \frac{d}{d x} (sin (x + y))

= e^{s i n (x + y)} \frac{d}{d x} (sin (x + y))

\frac{d}{d x} (sin (x + y)) = cos (x + y) (1 + \frac{d y}{d x})

= e^{s i n (x + y)} cos (x + y) (1 + \frac{d y}{d x})

Popular Examples

derivative of \sqrt[5]{x}-8/x

\frac{d}{d x} (5 x - \frac{8}{x})

limit as x approaches-3 of sqrt(4-x^2)

x \to - 3 lim (4 - x^{2})

integral of ((x-2)^2)/(sqrt(4x-x^2))

\int \frac{( x - 2 ) ^{2}}{4 x - x ^{2}} d x

(\partial)/(\partial x)(2xy^3+2xy-4)

\frac{\partial}{\partial x} (2 x y^{3} + 2 x y - 4)

derivative of f(x)=(x+2x^2)/(1+x^2)derivative of

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

Frequently Asked Questions (FAQ)

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