What is (\partial)/(\partial x)(x^{4cos(x)}) ?

The answer to (\partial)/(\partial x)(x^{4cos(x)}) is 4x^{4cos(x)}(-sin(x)ln(x)+(cos(x))/x)

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(\partial)/(\partial x)(x^{4cos(x)})

\frac{\partial}{\partial x} (x^{4 c o s (x)})

4 x^{4 c o s (x)} (- sin (x) ln (x) + \frac{cos ( x )}{x})

Solution steps

\frac{\partial}{\partial x} (x^{4 c o s (x)})

Apply exponent rule:

a^{b} = e^{b l n (a)}

x^{4 c o s (x)} = e^{4 c o s (x) l n (x)}

= \frac{\partial}{\partial x} (e^{4 c o s (x) l n (x)})

Apply the chain rule:

e^{4 c o s (x) l n (x)} \frac{\partial}{\partial x} (4 cos (x) ln (x))

= e^{4 c o s (x) l n (x)} \frac{\partial}{\partial x} (4 cos (x) ln (x))

\frac{\partial}{\partial x} (4 cos (x) ln (x)) = 4 (- sin (x) ln (x) + \frac{cos ( x )}{x})

= e^{4 c o s (x) l n (x)} \cdot 4 (- sin (x) ln (x) + \frac{cos ( x )}{x})

e^{4 c o s (x) l n (x)} = x^{4 c o s (x)}

= 4 x^{4 c o s (x)} (- sin (x) ln (x) + \frac{cos ( x )}{x})

\int \frac{4 + x ^{2}}{x ^{3}} d x

\frac{d Q}{d t} = 3 - \frac{3 Q}{1000}

f (x) = 4^{s i n^{2} (x) + c o s (3 x)}

x \to - 1 lim (∣ x ∣ - x)

y = π x

What is (\partial)/(\partial x)(x^{4cos(x)}) ?
The answer to (\partial)/(\partial x)(x^{4cos(x)}) is 4x^{4cos(x)}(-sin(x)ln(x)+(cos(x))/x)