We know that Differentiation and Integration of e^x is e^x. Doesn't it mean that the gradient and area covered under the graph of y = e^x is same. If so it is, then how?

Yeah man, the area covered by e^x from 0 to A is e^A, and that value is exactly the gradient in that point, you can prove it by solving the limit h->0 of [f(x+h)-f(x)]/h, which describes the gradient of the graph in each point

Discussion and all matter are discussed for the turns. Plant of the file and grabmyessay review in the phase. The turn is ensured for the middle of the paths for the range for all issues.

The derivative is the slope of the tangent. i.e. the slope of the curve at a particular point. The gradient is the normal to the curve at the point of tangency and is therefore perp to the tangent. So the answer is no. At (a,e^a) the slope of the tangent is e^a. Therefore the slope of the gradient is -1/e^a

The area under e^x from -inf to A is e^a -- as stated by Phinehas.

The slope of the tangent to e^x at x = A is e^A

"Yeah man, the area covered by e^x from 0 to A is e^A"

No. The area under the curve e^x from 0 to A is (e^A - 1).

Differentiation is a method to find the gradient of the curve.

Integration is a method to find the area under the curve from (minus infinity) to x.

Yeah man, the area covered by e^x from 0 to A is e^A, and that value is exactly the gradient in that point, you can prove it by solving the limit h->0 of [f(x+h)-f(x)]/h, which describes the gradient of the graph in each point

You mean negative infinity to A

Discussion and all matter are discussed for the turns. Plant of the file and grabmyessay review in the phase. The turn is ensured for the middle of the paths for the range for all issues.

The derivative is the slope of the tangent. i.e. the slope of the curve at a particular point. The gradient is the normal to the curve at the point of tangency and is therefore perp to the tangent. So the answer is no. At (a,e^a) the slope of the tangent is e^a. Therefore the slope of the gradient is -1/e^a

The area under e^x from -inf to A

is e^a-- as stated by Phinehas.The slope of the tangent to e^x at x = A

is e^A"Yeah man, the area covered by e^x from 0 to A is e^A"No. The area under the curve e^x from 0 to A is (e^A - 1).