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# What is the derivative of e to the u?

Updated: 4/28/2022

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15y ago

(eu)'=ueu-1

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15y ago

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Q: What is the derivative of e to the u?
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### How do you do exponential functions?

The derivative of e^u(x) with respect to x: [du/dx]*[e^u(x)]For a general exponential: b^x, can be rewritten as b^x = e^(x*ln(b))So derivative of b^x = derivative of e^u(x), where u(x) = x*ln(b).Derivative of x*ln(b) = ln(b). {remember b is just a constant, so ln(b) is a constant}So derivative of b^x = ln(b)*e^(x*ln(b))= ln(b) * b^x(from above)

### How do you differentiate exponential function?

The derivative of e^u(x) with respect to x: [du/dx]*[e^u(x)]For a general exponential: b^x, can be rewritten as b^x = e^(x*ln(b))So derivative of b^x = derivative of e^u(x), where u(x) = x*ln(b).Derivative of x*ln(b) = ln(b). {remember b is just a constant, so ln(b) is a constant}So derivative of b^x = ln(b)*e^(x*ln(b))= ln(b) * b^x(from above)

### What is the derivative of tangent?

the derivative of tangent dy/dx [ tan(u) ]= [sec^(2)u]u' this means that the derivative of tangent of u is secant squared u times the derivative of u.

### What is the derivative of e to the e?

ee is a constant and so its derivative is 0.

### What is the derivative of e to the power of -2 times x?

e^(-2x) * -2 The derivative of e^F(x) is e^F(x) times the derivative of F(x)

### What is the derivitive of e?

2.71828183 ==So the derivative of a constant is zero.If you have e^x, the derivative is e^x.

### What is the derivative of xe?

The derivative of xe is e. The derivative of xe is exe-1.

### What is the derivative of e to the power of x?

The derivative of ex is ex

### What is the first derivative of e raised to the power of x?

The first derivative of e to the x power is e to the power of x.

### What is the derivative of 23te-1.2t?

You must first apply the product rule to the term: 23te Product Rule: y=uv= u(dv/dx) + v(du/dx) *the derivative of e^x is still e^x and since your 'x' value is one, the derivative of 'e ^1' stays as 'e' plug it in: y = 23t (e) + 23 (e) then include the derivation of your last term: -1.2t ---&gt; -1.2 answer: y = 23te + 23e -1.2

### What is the differential of Ln?

the derivative of Ln(u)=u'/u