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Popular >

derivative of sin(x^{cos(x}))

Solution

\frac{d}{d x} (sin (x^{c o s (x)}))

Solution

cos (x^{c o s (x)}) x^{c o s (x)} (- sin (x) ln (x) + \frac{cos ( x )}{x})

Solution steps

\frac{d}{d x} (sin (x^{c o s (x)}))

Apply the chain rule:

cos (x^{c o s (x)}) \frac{d}{d x} (x^{c o s (x)})

= cos (x^{c o s (x)}) \frac{d}{d x} (x^{c o s (x)})

\frac{d}{d x} (x^{c o s (x)}) = x^{c o s (x)} (- sin (x) ln (x) + \frac{cos ( x )}{x})

= cos (x^{c o s (x)}) x^{c o s (x)} (- sin (x) ln (x) + \frac{cos ( x )}{x})

Popular Examples

y^{^{'}} = 3 + e^{- 2 t}

laplacetransform t^2sin(4t)laplace transform

t^{2} sin (4 t)

(dy)/(dt)+e^ty=12e^t

\frac{d y}{d t} + e^{t} y = 12 e^{t}

derivative of x/7+7/x derivative of

\frac{x}{7} + \frac{7}{x}

inverse oflaplace F(s)=(s+9)/(s^2-2s-3)inverse laplace

F (s) = \frac{s + 9}{s ^{2} - 2 s - 3}

Frequently Asked Questions (FAQ)

What is the derivative of sin(x^{cos(x})) ?
The derivative of sin(x^{cos(x})) is cos(x^{cos(x)})x^{cos(x)}(-sin(x)ln(x)+(cos(x))/x)
What is the first derivative of sin(x^{cos(x})) ?
The first derivative of sin(x^{cos(x})) is cos(x^{cos(x)})x^{cos(x)}(-sin(x)ln(x)+(cos(x))/x)