To find the derivative of the function h(x)=sin(2x)+cos(x^2)+e^(x^3) at x=0, we need to apply the chain rule and the power rule.

The derivative of sin(2x) with respect to x is 2cos(2x).
The derivative of cos(x^2) with respect to x is -2xsin(x^2).
The derivative of e^(x^3) with respect to x is 3x^2e^(x^3).

So, the derivative of h(x) is h'(x)=2cos(2x)-2xsin(x^2)+3x^2e^(x^3).

To find h'(0), we substitute x=0 into h'(x):

h'(0)=2cos(2*0)-2*0*sin(0^2)+3*0^2*e^(0^3)
=2cos(0)-0+0
=2*1-0+0
=2.

So, h'(0)=2.

Question

To find the derivative of the function h(x)=sin(2x)+cos(x^2)+e^(x^3) at x=0, we need to apply the chain rule and the power rule.

The derivative of sin(2x) with respect to x is 2cos(2x).
The derivative of cos(x^2) with respect to x is -2xsin(x^2).
The derivative of e^(x^3) with respect to x is 3x^2e^(x^3).

So, the derivative of h(x) is h'(x)=2cos(2x)-2xsin(x^2)+3x^2e^(x^3).

To find h'(0), we substitute x=0 into h'(x):

h'(0)=2cos(2*0)-2*0*sin(0^2)+3*0^2*e^(0^3)
     =2cos(0)-0+0
     =2*1-0+0
     =2.

So, h'(0)=2.

Knowee AI · Accepted Answer

To find the derivative of the function h(x)=sin(2x)+cos(x^2)+e^(x^3) at x=0, we need to apply the chain rule and the power rule.

The derivative of sin(2x) with respect to x is 2cos(2x).
The derivative of cos(x^2) with respect to x is -2xsin(x^2).
The derivative of e^(x^3) with respect to x is 3x^2e^(x^3).

So, the derivative of h(x) is h'(x)=2cos(2x)-2xsin(x^2)+3x^2e^(x^3).

To find h'(0), we substitute x=0 into h'(x):

h'(0)=2cos(2*0)-2*0*sin(0^2)+3*0^2*e^(0^3)
     =2cos(0)-0+0
     =2*1-0+0
     =2.

So, h'(0)=2.

Consider the function h(x)=sin(2x)+cos(x2)+ex3ℎ(𝑥)=sin⁡(2𝑥)+cos⁡(𝑥2)+𝑒𝑥3. Then h′(0)=ℎ′(0)= Answer 1 Question 3.

Question

Solution

Similar Questions

Upgrade your grade with Knowee