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Popular >

derivative of f(x)=e^{ln(x)}-e^{5ln(x^2)}

Solution

derivative of

f (x) = e^{l n (x)} - e^{5 l n (x^{2})}

Solution

1 - 10 x^{9}

Solution steps

\frac{d}{d x} (e^{l n (x)} - e^{5 l n (x^{2})})

Simplify

e^{l n (x)} - e^{5 l n (x^{2})} : x - x^{10}

= \frac{d}{d x} (x - x^{10})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d x}{d x} - \frac{d}{d x} (x^{10})

\frac{d x}{d x} = 1

\frac{d}{d x} (x^{10}) = 10 x^{9}

= 1 - 10 x^{9}

Popular Examples

derivative of f(x)=tan(x)cot(x)derivative of

f (x) = tan (x) cot (x)

derivative of 3/((x-4^2))

\frac{d}{d x} (\frac{3}{( x - 4 ) ^{2}})

derivative of arcsin(1/2 x)

\frac{d}{d x} (arcsin (\frac{1}{2} x))

(\partial)/(\partial x)(arctan(x/3))

\frac{\partial}{\partial x} (arctan (\frac{x}{3}))

limit as x approaches-3+of x/(x^2-9)

x \to - 3 + lim (\frac{x}{x ^{2} - 9})

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=e^{ln(x)}-e^{5ln(x^2)} ?
The derivative of f(x)=e^{ln(x)}-e^{5ln(x^2)} is 1-10x^9
What is the first derivative of f(x)=e^{ln(x)}-e^{5ln(x^2)} ?
The first derivative of f(x)=e^{ln(x)}-e^{5ln(x^2)} is 1-10x^9