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Popular >

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

Solution

\frac{d}{d x} (cos (x^{s i n (x)}))

Solution

- sin (x^{s i n (x)}) x^{s i n (x)} (cos (x) ln (x) + \frac{sin ( x )}{x})

Solution steps

\frac{d}{d x} (cos (x^{s i n (x)}))

Apply the chain rule:

- sin (x^{s i n (x)}) \frac{d}{d x} (x^{s i n (x)})

= - sin (x^{s i n (x)}) \frac{d}{d x} (x^{s i n (x)})

\frac{d}{d x} (x^{s i n (x)}) = x^{s i n (x)} (cos (x) ln (x) + \frac{sin ( x )}{x})

= - sin (x^{s i n (x)}) x^{s i n (x)} (cos (x) ln (x) + \frac{sin ( x )}{x})

Popular Examples

derivative of x^4-50x^2

\frac{d}{d x} (x^{4} - 50 x^{2})

(\partial)/(\partial x)(2x^2+2y-8)

\frac{\partial}{\partial x} (2 x^{2} + 2 y - 8)

tangent of f(x)=sqrt(5x+6),(2,4)tangent of

f (x) = 5 x + 6, (2, 4)

laplacetransform t*sin(t)laplace transform

t \cdot sin (t)

derivative of sin(2x+3ln(e)+4sqrt(x))

\frac{d}{d x} (sin (2 x) + 3 ln (e) + 4 x)

Frequently Asked Questions (FAQ)

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